Example #1
0
/* Make an RSA key for size bits, with e specified, 65537 is a good e */
int MakeRsaKey(RsaKey* key, int size, long e, RNG* rng)
{
    mp_int p, q, tmp1, tmp2, tmp3;
    int    err;

    if (key == NULL || rng == NULL)
        return BAD_FUNC_ARG;

    if (size < RSA_MIN_SIZE || size > RSA_MAX_SIZE)
        return BAD_FUNC_ARG;

    if (e < 3 || (e & 1) == 0)
        return BAD_FUNC_ARG;

    if ((err = mp_init_multi(&p, &q, &tmp1, &tmp2, &tmp3, NULL)) != MP_OKAY)
        return err;

    err = mp_set_int(&tmp3, e);

    /* make p */
    if (err == MP_OKAY) {
        do {
            err = rand_prime(&p, size/16, rng, key->heap); /* size in bytes/2 */

            if (err == MP_OKAY)
                err = mp_sub_d(&p, 1, &tmp1);  /* tmp1 = p-1 */

            if (err == MP_OKAY)
                err = mp_gcd(&tmp1, &tmp3, &tmp2);  /* tmp2 = gcd(p-1, e) */
        } while (err == MP_OKAY && mp_cmp_d(&tmp2, 1) != 0);  /* e divdes p-1 */
    }

    /* make q */
    if (err == MP_OKAY) {
        do {
            err = rand_prime(&q, size/16, rng, key->heap); /* size in bytes/2 */

            if (err == MP_OKAY)
                err = mp_sub_d(&q, 1, &tmp1);  /* tmp1 = q-1 */

            if (err == MP_OKAY)
                err = mp_gcd(&tmp1, &tmp3, &tmp2);  /* tmp2 = gcd(q-1, e) */
        } while (err == MP_OKAY && mp_cmp_d(&tmp2, 1) != 0);  /* e divdes q-1 */
    }

    if (err == MP_OKAY)
        err = mp_init_multi(&key->n, &key->e, &key->d, &key->p, &key->q, NULL);

    if (err == MP_OKAY)
        err = mp_init_multi(&key->dP, &key->dQ, &key->u, NULL, NULL, NULL);

    if (err == MP_OKAY)
        err = mp_sub_d(&p, 1, &tmp2);  /* tmp2 = p-1 */

    if (err == MP_OKAY)
        err = mp_lcm(&tmp1, &tmp2, &tmp1);  /* tmp1 = lcm(p-1, q-1),last loop */

    /* make key */
    if (err == MP_OKAY)
        err = mp_set_int(&key->e, e);  /* key->e = e */

    if (err == MP_OKAY)                /* key->d = 1/e mod lcm(p-1, q-1) */
        err = mp_invmod(&key->e, &tmp1, &key->d);

    if (err == MP_OKAY)
        err = mp_mul(&p, &q, &key->n);  /* key->n = pq */

    if (err == MP_OKAY)
        err = mp_sub_d(&p, 1, &tmp1);

    if (err == MP_OKAY)
        err = mp_sub_d(&q, 1, &tmp2);

    if (err == MP_OKAY)
        err = mp_mod(&key->d, &tmp1, &key->dP);

    if (err == MP_OKAY)
        err = mp_mod(&key->d, &tmp2, &key->dQ);

    if (err == MP_OKAY)
        err = mp_invmod(&q, &p, &key->u);

    if (err == MP_OKAY)
        err = mp_copy(&p, &key->p);

    if (err == MP_OKAY)
        err = mp_copy(&q, &key->q);

    if (err == MP_OKAY)
        key->type = RSA_PRIVATE; 

    mp_clear(&tmp3); 
    mp_clear(&tmp2); 
    mp_clear(&tmp1); 
    mp_clear(&q); 
    mp_clear(&p);

    if (err != MP_OKAY) {
        FreeRsaKey(key);        
        return err;
    }

    return 0;
}
Example #2
0
static SECStatus
rsa_keygen_from_primes(mp_int *p, mp_int *q, mp_int *e, RSAPrivateKey *key,
                       unsigned int keySizeInBits)
{
    mp_int n, d, phi;
    mp_int psub1, qsub1, tmp;
    mp_err   err = MP_OKAY;
    SECStatus rv = SECSuccess;
    MP_DIGITS(&n)     = 0;
    MP_DIGITS(&d)     = 0;
    MP_DIGITS(&phi)   = 0;
    MP_DIGITS(&psub1) = 0;
    MP_DIGITS(&qsub1) = 0;
    MP_DIGITS(&tmp)   = 0;
    CHECK_MPI_OK( mp_init(&n)     );
    CHECK_MPI_OK( mp_init(&d)     );
    CHECK_MPI_OK( mp_init(&phi)   );
    CHECK_MPI_OK( mp_init(&psub1) );
    CHECK_MPI_OK( mp_init(&qsub1) );
    CHECK_MPI_OK( mp_init(&tmp)   );
    /* 1.  Compute n = p*q */
    CHECK_MPI_OK( mp_mul(p, q, &n) );
    /*     verify that the modulus has the desired number of bits */
    if ((unsigned)mpl_significant_bits(&n) != keySizeInBits) {
	PORT_SetError(SEC_ERROR_NEED_RANDOM);
	rv = SECFailure;
	goto cleanup;
    }
    /* 2.  Compute phi = (p-1)*(q-1) */
    CHECK_MPI_OK( mp_sub_d(p, 1, &psub1) );
    CHECK_MPI_OK( mp_sub_d(q, 1, &qsub1) );
    CHECK_MPI_OK( mp_mul(&psub1, &qsub1, &phi) );
    /* 3.  Compute d = e**-1 mod(phi) */
    err = mp_invmod(e, &phi, &d);
    /*     Verify that phi(n) and e have no common divisors */
    if (err != MP_OKAY) {
	if (err == MP_UNDEF) {
	    PORT_SetError(SEC_ERROR_NEED_RANDOM);
	    err = MP_OKAY; /* to keep PORT_SetError from being called again */
	    rv = SECFailure;
	}
	goto cleanup;
    }
    MPINT_TO_SECITEM(&n, &key->modulus, key->arena);
    MPINT_TO_SECITEM(&d, &key->privateExponent, key->arena);
    /* 4.  Compute exponent1 = d mod (p-1) */
    CHECK_MPI_OK( mp_mod(&d, &psub1, &tmp) );
    MPINT_TO_SECITEM(&tmp, &key->exponent1, key->arena);
    /* 5.  Compute exponent2 = d mod (q-1) */
    CHECK_MPI_OK( mp_mod(&d, &qsub1, &tmp) );
    MPINT_TO_SECITEM(&tmp, &key->exponent2, key->arena);
    /* 6.  Compute coefficient = q**-1 mod p */
    CHECK_MPI_OK( mp_invmod(q, p, &tmp) );
    MPINT_TO_SECITEM(&tmp, &key->coefficient, key->arena);
cleanup:
    mp_clear(&n);
    mp_clear(&d);
    mp_clear(&phi);
    mp_clear(&psub1);
    mp_clear(&qsub1);
    mp_clear(&tmp);
    if (err) {
	MP_TO_SEC_ERROR(err);
	rv = SECFailure;
    }
    return rv;
}
Example #3
0
int DsaSign(const byte* digest, byte* out, DsaKey* key, RNG* rng)
{
    mp_int k, kInv, r, s, H;
    int    ret = 0, sz;
    byte   buffer[DSA_HALF_SIZE];

    if (mp_init_multi(&k, &kInv, &r, &s, &H, 0) != MP_OKAY)
        return MP_INIT_E;

    sz = min(sizeof(buffer), mp_unsigned_bin_size(&key->q)); 

    /* generate k */
    RNG_GenerateBlock(rng, buffer, sz);
    buffer[0] |= 0x0C;

    if (mp_read_unsigned_bin(&k, buffer, sz) != MP_OKAY)
        ret = MP_READ_E;

    if (mp_cmp_d(&k, 1) != MP_GT) assert(0);

    /* inverse k mod q */
    if (ret == 0 && mp_invmod(&k, &key->q, &kInv) != MP_OKAY)
        ret = MP_INVMOD_E;

    /* generate r, r = (g exp k mod p) mod q */
    if (ret == 0 && mp_exptmod(&key->g, &k, &key->p, &r) != MP_OKAY)
        ret = MP_EXPTMOD_E;

    if (ret == 0 && mp_mod(&r, &key->q, &r) != MP_OKAY)
        ret = MP_MOD_E;

    /* generate H from sha digest */
    if (ret == 0 && mp_read_unsigned_bin(&H, digest,SHA_DIGEST_SIZE) != MP_OKAY)
        ret = MP_READ_E;

    /* generate s, s = (kInv * (H + x*r)) % q */
    if (ret == 0 && mp_mul(&key->x, &r, &s) != MP_OKAY)
        ret = MP_MUL_E;

    if (ret == 0 && mp_add(&s, &H, &s) != MP_OKAY)
        ret = MP_ADD_E;

    if (ret == 0 && mp_mulmod(&s, &kInv, &key->q, &s) != MP_OKAY)
        ret = MP_MULMOD_E;

    /* write out */
    if (ret == 0)  {
        int rSz = mp_unsigned_bin_size(&r);
        int sSz = mp_unsigned_bin_size(&s);

        if (rSz == DSA_HALF_SIZE - 1) {
            out[0] = 0;
            out++;
        }

        if (mp_to_unsigned_bin(&r, out) != MP_OKAY)
            ret = MP_TO_E;
        else {
            if (sSz == DSA_HALF_SIZE - 1) {
                out[rSz] = 0;
                out++;
            }    
            ret = mp_to_unsigned_bin(&s, out + rSz);
        }
    }

    mp_clear(&H);
    mp_clear(&s);
    mp_clear(&r);
    mp_clear(&kInv);
    mp_clear(&k);

    return ret;
}
Example #4
0
/*------------------------------------------------------------------*/
int32 read_poly(msieve_obj *obj, mp_t *n,
	       mp_poly_t *rat_poly,
	       mp_poly_t *alg_poly,
	       double *skewness) {
	
	int32 i;
	FILE *fp;
	char buf[LINE_BUF_SIZE];
	mp_t read_n;
	signed_mp_t val, rpow, tmp;

	fp = fopen(obj->nfs_fbfile_name, "r");
	if (fp == NULL)
		return -1;
	
	buf[0] = 0;
	fgets(buf, (int)sizeof(buf), fp);
	if (buf[0] != 'N') {
		fclose(fp);
		logprintf(obj, "warning: factor base file uninitialized\n");
		return -1;
	}

	/* check that the polynomial is for the 
	   right number */

	mp_str2mp(buf + 2, &read_n, 10);
	if (mp_cmp(&read_n, n)) {
		fclose(fp);
		logprintf(obj, "warning: NFS input not found in "
				"factor base file\n");
		return -1;
	}

	/* read in skewness if present */

	fgets(buf, (int)sizeof(buf), fp);
	if (buf[0] == 'S') {
		if (skewness != NULL)
			*skewness = atof(buf + 5);
		fgets(buf, (int)sizeof(buf), fp);
	}
	else if (skewness != NULL) {
		*skewness = 1.0;
	}

	/* read one coefficient per line; 'R<number>' is
	   for rational coefficients, 'A<number>' for algebraic */

	while ((buf[0] == 'R' || buf[0] == 'A') && isdigit(buf[1])) {
		signed_mp_t *read_coeff;
		char *tmp;

		i = buf[1] - '0';
		if (i > MAX_POLY_DEGREE) {
			fclose(fp);
			logprintf(obj, "warning: polynomial degree exceeds "
					"%d\n", MAX_POLY_DEGREE);
			exit(-1);
		}

		if (buf[0] == 'R')
			read_coeff = rat_poly->coeff + i;
		else
			read_coeff = alg_poly->coeff + i;

		tmp = buf + 2;
		while (isspace(*tmp))
			tmp++;

		if (*tmp == '-') {
			read_coeff->sign = NEGATIVE;
			tmp++;
		}
		else {
			read_coeff->sign = POSITIVE;
		}
		mp_str2mp(tmp, &read_coeff->num, 10);
		if (fgets(buf, (int)sizeof(buf), fp) == NULL)
			break;
	}

	for (i = MAX_POLY_DEGREE; i >= 0; i--) {
		if (!mp_is_zero(&rat_poly->coeff[i].num))
			break;
	}
	if (i > 0)
		rat_poly->degree = i;

	for (i = MAX_POLY_DEGREE; i >= 0; i--) {
		if (!mp_is_zero(&alg_poly->coeff[i].num))
			break;
	}
	if (i > 0)
		alg_poly->degree = i;

	fclose(fp);

	if (rat_poly->degree == 0 || alg_poly->degree == 0) {
		logprintf(obj, "error: polynomial is missing or corrupt\n");
		exit(-1);
	}
	if (rat_poly->degree != 1) {
		logprintf(obj, "error: no support for nonlinear "
				"rational polynomials\n");
		exit(-1);
	}
	
	/* plug the rational polynomial coefficients into the 
	   algebraic polynomial */

	i = alg_poly->degree;
	signed_mp_copy(alg_poly->coeff + i, &val);
	signed_mp_copy(rat_poly->coeff + 1, &rpow);

	for (i--; i >= 0; i--) {
		signed_mp_mul(&val, rat_poly->coeff + 0, &tmp);
		tmp.sign = (tmp.sign == POSITIVE) ? NEGATIVE : POSITIVE;
		signed_mp_copy(&tmp, &val);

		signed_mp_mul(alg_poly->coeff + i, &rpow, &tmp);
		signed_mp_add(&val, &tmp, &val);

		signed_mp_mul(rat_poly->coeff + 1, &rpow, &tmp);
		signed_mp_copy(&tmp, &rpow);
	}

	/* verify that |result| >= N, and that result % N == 0. 
	   The only place where we do any mod-N arithmetic is the 
	   NFS square root, which will not work if N has additional 
	   factors that are not reflected in the polynomials */

	if ((i = mp_cmp(&val.num, n)) < 0) {
		logprintf(obj, "error: NFS input does not match polynomials\n");
		logprintf(obj, "check that input doesn't have small factors\n");
		exit(-1);
	}
	else if (i > 0) {
		mp_mod(&val.num, n, &read_n);
		if (!mp_is_zero(&read_n)) {
			logprintf(obj, "error: NFS input does not "
					"match polynomials\n");
			exit(-1);
		}
	}

	return 0;
}
Example #5
0
File: timing.c Project: asr/uhc
int main(void)
{
   ulong64 tt, gg, CLK_PER_SEC;
   FILE *log, *logb, *logc, *logd;
   mp_int a, b, c, d, e, f;
   int n, cnt, ix, old_kara_m, old_kara_s;
   unsigned rr;

   mp_init(&a);
   mp_init(&b);
   mp_init(&c);
   mp_init(&d);
   mp_init(&e);
   mp_init(&f);

   srand(time(NULL));


   /* temp. turn off TOOM */
   TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000;

   CLK_PER_SEC = TIMFUNC();
   sleep(1);
   CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC;

   printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC);
   goto exptmod;
   log = fopen("logs/add.log", "w");
   for (cnt = 8; cnt <= 128; cnt += 8) {
      SLEEP;
      mp_rand(&a, cnt);
      mp_rand(&b, cnt);
      rr = 0;
      tt = -1;
      do {
	 gg = TIMFUNC();
	 DO(mp_add(&a, &b, &c));
	 gg = (TIMFUNC() - gg) >> 1;
	 if (tt > gg)
	    tt = gg;
      } while (++rr < 100000);
      printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
      fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
      fflush(log);
   }
   fclose(log);

   log = fopen("logs/sub.log", "w");
   for (cnt = 8; cnt <= 128; cnt += 8) {
      SLEEP;
      mp_rand(&a, cnt);
      mp_rand(&b, cnt);
      rr = 0;
      tt = -1;
      do {
	 gg = TIMFUNC();
	 DO(mp_sub(&a, &b, &c));
	 gg = (TIMFUNC() - gg) >> 1;
	 if (tt > gg)
	    tt = gg;
      } while (++rr < 100000);

      printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
      fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
      fflush(log);
   }
   fclose(log);

   /* do mult/square twice, first without karatsuba and second with */
 multtest:
   old_kara_m = KARATSUBA_MUL_CUTOFF;
   old_kara_s = KARATSUBA_SQR_CUTOFF;
   for (ix = 0; ix < 2; ix++) {
      printf("With%s Karatsuba\n", (ix == 0) ? "out" : "");

      KARATSUBA_MUL_CUTOFF = (ix == 0) ? 9999 : old_kara_m;
      KARATSUBA_SQR_CUTOFF = (ix == 0) ? 9999 : old_kara_s;

      log = fopen((ix == 0) ? "logs/mult.log" : "logs/mult_kara.log", "w");
      for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
	 SLEEP;
	 mp_rand(&a, cnt);
	 mp_rand(&b, cnt);
	 rr = 0;
	 tt = -1;
	 do {
	    gg = TIMFUNC();
	    DO(mp_mul(&a, &b, &c));
	    gg = (TIMFUNC() - gg) >> 1;
	    if (tt > gg)
	       tt = gg;
	 } while (++rr < 100);
	 printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n",
		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
	 fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);
	 fflush(log);
      }
      fclose(log);

      log = fopen((ix == 0) ? "logs/sqr.log" : "logs/sqr_kara.log", "w");
      for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
	 SLEEP;
	 mp_rand(&a, cnt);
	 rr = 0;
	 tt = -1;
	 do {
	    gg = TIMFUNC();
	    DO(mp_sqr(&a, &b));
	    gg = (TIMFUNC() - gg) >> 1;
	    if (tt > gg)
	       tt = gg;
	 } while (++rr < 100);
	 printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n",
		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
	 fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);
	 fflush(log);
      }
      fclose(log);

   }
 exptmod:

   {
      char *primes[] = {
	 /* 2K large moduli */
	 "179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586239334100047359817950870678242457666208137217",
	 "32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638099733077152121140120031150424541696791951097529546801429027668869927491725169",
	 "1044388881413152506691752710716624382579964249047383780384233483283953907971557456848826811934997558340890106714439262837987573438185793607263236087851365277945956976543709998340361590134383718314428070011855946226376318839397712745672334684344586617496807908705803704071284048740118609114467977783598029006686938976881787785946905630190260940599579453432823469303026696443059025015972399867714215541693835559885291486318237914434496734087811872639496475100189041349008417061675093668333850551032972088269550769983616369411933015213796825837188091833656751221318492846368125550225998300412344784862595674492194617023806505913245610825731835380087608622102834270197698202313169017678006675195485079921636419370285375124784014907159135459982790513399611551794271106831134090584272884279791554849782954323534517065223269061394905987693002122963395687782878948440616007412945674919823050571642377154816321380631045902916136926708342856440730447899971901781465763473223850267253059899795996090799469201774624817718449867455659250178329070473119433165550807568221846571746373296884912819520317457002440926616910874148385078411929804522981857338977648103126085902995208257421855249796721729039744118165938433694823325696642096892124547425283",
	 /* 2K moduli mersenne primes */
	 "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151",
	 "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127",
	 "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087",
	 "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007",
	 "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071",
	 "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991",

	 /* DR moduli */
	 "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079",
	 "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039",
	 "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431",
	 "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783",
	 "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147",
	 "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503",
	 "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679",

	 /* generic unrestricted moduli */
	 "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203",
	 "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487",
	 "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
	 "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
	 "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
	 "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
	 "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
	 NULL
      };
      log = fopen("logs/expt.log", "w");
      logb = fopen("logs/expt_dr.log", "w");
      logc = fopen("logs/expt_2k.log", "w");
      logd = fopen("logs/expt_2kl.log", "w");
      for (n = 0; primes[n]; n++) {
	 SLEEP;
	 mp_read_radix(&a, primes[n], 10);
	 mp_zero(&b);
	 for (rr = 0; rr < (unsigned) mp_count_bits(&a); rr++) {
	    mp_mul_2(&b, &b);
	    OR_DIGIT(&b,0,lbit()) ;
	    INC_USED(&b,1) ;
	 }
	 mp_sub_d(&a, 1, &c);
	 mp_mod(&b, &c, &b);
	 mp_set(&c, 3);
	 rr = 0;
	 tt = -1;
	 do {
	    gg = TIMFUNC();
	    DO(mp_exptmod(&c, &b, &a, &d));
	    gg = (TIMFUNC() - gg) >> 1;
	    if (tt > gg)
	       tt = gg;
	 } while (++rr < 10);
	 mp_sub_d(&a, 1, &e);
	 mp_sub(&e, &b, &b);
	 mp_exptmod(&c, &b, &a, &e);	/* c^(p-1-b) mod a */
	 mp_mulmod(&e, &d, &a, &d);	/* c^b * c^(p-1-b) == c^p-1 == 1 */
	 if (mp_cmp_d(&d, 1)) {
	    printf("Different (%d)!!!\n", mp_count_bits(&a));
	    draw(&d);
	    exit(0);
	 }
	 printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n",
		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
	 fprintf(n < 4 ? logd : (n < 9) ? logc : (n < 16) ? logb : log,
		 "%d %9llu\n", mp_count_bits(&a), tt);
      }
   }
   fclose(log);
   fclose(logb);
   fclose(logc);
   fclose(logd);

   log = fopen("logs/invmod.log", "w");
   for (cnt = 4; cnt <= 128; cnt += 4) {
      SLEEP;
      mp_rand(&a, cnt);
      mp_rand(&b, cnt);

      do {
	 mp_add_d(&b, 1, &b);
	 mp_gcd(&a, &b, &c);
      } while (mp_cmp_d(&c, 1) != MP_EQ);

      rr = 0;
      tt = -1;
      do {
	 gg = TIMFUNC();
	 DO(mp_invmod(&b, &a, &c));
	 gg = (TIMFUNC() - gg) >> 1;
	 if (tt > gg)
	    tt = gg;
      } while (++rr < 1000);
      mp_mulmod(&b, &c, &a, &d);
      if (mp_cmp_d(&d, 1) != MP_EQ) {
	 printf("Failed to invert\n");
	 return 0;
      }
      printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n",
	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
      fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
   }
   fclose(log);

   return 0;
}
Example #6
0
File: demo.c Project: das/tcl
int main(void)
{
   mp_int a, b, c, d, e, f;
   unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n, inv_n,
                 div2_n, mul2_n, add_d_n, sub_d_n, t;
   unsigned rr;
   int i, n, err, cnt, ix, old_kara_m, old_kara_s;


   mp_init(&a);
   mp_init(&b);
   mp_init(&c);
   mp_init(&d);
   mp_init(&e);
   mp_init(&f);

   srand(time(NULL));

#if 0
  // test mp_get_int
  printf("Testing: mp_get_int\n");
  for(i=0;i<1000;++i) {
    t = ((unsigned long)rand()*rand()+1)&0xFFFFFFFF;
    mp_set_int(&a,t);
    if (t!=mp_get_int(&a)) { 
      printf("mp_get_int() bad result!\n");
      return 1;
    }
  }
  mp_set_int(&a,0);
  if (mp_get_int(&a)!=0)
  { printf("mp_get_int() bad result!\n");
    return 1;
  }
  mp_set_int(&a,0xffffffff);
  if (mp_get_int(&a)!=0xffffffff)
  { printf("mp_get_int() bad result!\n");
    return 1;
  }

  // test mp_sqrt
  printf("Testing: mp_sqrt\n");
  for (i=0;i<1000;++i) { 
    printf("%6d\r", i); fflush(stdout);
    n = (rand()&15)+1;
    mp_rand(&a,n);
    if (mp_sqrt(&a,&b) != MP_OKAY)
    { printf("mp_sqrt() error!\n");
      return 1;
    }
    mp_n_root(&a,2,&a);
    if (mp_cmp_mag(&b,&a) != MP_EQ)
    { printf("mp_sqrt() bad result!\n");
      return 1;
    }
  }

  printf("\nTesting: mp_is_square\n");
  for (i=0;i<1000;++i) {
    printf("%6d\r", i); fflush(stdout);

    /* test mp_is_square false negatives */
    n = (rand()&7)+1;
    mp_rand(&a,n);
    mp_sqr(&a,&a);
    if (mp_is_square(&a,&n)!=MP_OKAY) { 
      printf("fn:mp_is_square() error!\n");
      return 1;
    }
    if (n==0) { 
      printf("fn:mp_is_square() bad result!\n");
      return 1;
    }

    /* test for false positives */
    mp_add_d(&a, 1, &a);
    if (mp_is_square(&a,&n)!=MP_OKAY) { 
      printf("fp:mp_is_square() error!\n");
      return 1;
    }
    if (n==1) { 
      printf("fp:mp_is_square() bad result!\n");
      return 1;
    }

  }
  printf("\n\n");

   /* test for size */
   for (ix = 10; ix < 256; ix++) {
       printf("Testing (not safe-prime): %9d bits    \r", ix); fflush(stdout);
       err = mp_prime_random_ex(&a, 8, ix, (rand()&1)?LTM_PRIME_2MSB_OFF:LTM_PRIME_2MSB_ON, myrng, NULL);
       if (err != MP_OKAY) {
          printf("failed with err code %d\n", err);
          return EXIT_FAILURE;
       }
       if (mp_count_bits(&a) != ix) {
          printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
          return EXIT_FAILURE;
       }
   }

   for (ix = 16; ix < 256; ix++) {
       printf("Testing (   safe-prime): %9d bits    \r", ix); fflush(stdout);
       err = mp_prime_random_ex(&a, 8, ix, ((rand()&1)?LTM_PRIME_2MSB_OFF:LTM_PRIME_2MSB_ON)|LTM_PRIME_SAFE, myrng, NULL);
       if (err != MP_OKAY) {
          printf("failed with err code %d\n", err);
          return EXIT_FAILURE;
       }
       if (mp_count_bits(&a) != ix) {
          printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
          return EXIT_FAILURE;
       }
       /* let's see if it's really a safe prime */
       mp_sub_d(&a, 1, &a);
       mp_div_2(&a, &a);
       mp_prime_is_prime(&a, 8, &cnt);
       if (cnt != MP_YES) {
          printf("sub is not prime!\n");
          return EXIT_FAILURE;
       }
   }

   printf("\n\n");

   mp_read_radix(&a, "123456", 10);
   mp_toradix_n(&a, buf, 10, 3);
   printf("a == %s\n", buf);
   mp_toradix_n(&a, buf, 10, 4);
   printf("a == %s\n", buf);
   mp_toradix_n(&a, buf, 10, 30);
   printf("a == %s\n", buf);


#if 0
   for (;;) {
      fgets(buf, sizeof(buf), stdin);
      mp_read_radix(&a, buf, 10);
      mp_prime_next_prime(&a, 5, 1);
      mp_toradix(&a, buf, 10);
      printf("%s, %lu\n", buf, a.dp[0] & 3);
   }
#endif

   /* test mp_cnt_lsb */
   printf("testing mp_cnt_lsb...\n");
   mp_set(&a, 1);
   for (ix = 0; ix < 1024; ix++) {
       if (mp_cnt_lsb(&a) != ix) {
          printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a));
          return 0;
       }
       mp_mul_2(&a, &a);
   }

/* test mp_reduce_2k */
   printf("Testing mp_reduce_2k...\n");
   for (cnt = 3; cnt <= 128; ++cnt) {
       mp_digit tmp;
       mp_2expt(&a, cnt);
       mp_sub_d(&a, 2, &a);  /* a = 2**cnt - 2 */


       printf("\nTesting %4d bits", cnt);
       printf("(%d)", mp_reduce_is_2k(&a));
       mp_reduce_2k_setup(&a, &tmp);
       printf("(%d)", tmp);
       for (ix = 0; ix < 1000; ix++) {
           if (!(ix & 127)) {printf("."); fflush(stdout); }
           mp_rand(&b, (cnt/DIGIT_BIT  + 1) * 2);
           mp_copy(&c, &b);
           mp_mod(&c, &a, &c);
           mp_reduce_2k(&b, &a, 1);
           if (mp_cmp(&c, &b)) {
              printf("FAILED\n");
              exit(0);
           }
        }
    }

/* test mp_div_3  */
   printf("Testing mp_div_3...\n");
   mp_set(&d, 3);
   for (cnt = 0; cnt < 10000; ) {
      mp_digit r1, r2;

      if (!(++cnt & 127)) printf("%9d\r", cnt);
      mp_rand(&a, abs(rand()) % 128 + 1);
      mp_div(&a, &d, &b, &e);
      mp_div_3(&a, &c, &r2);

      if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) {
         printf("\n\nmp_div_3 => Failure\n");
      }
   }
   printf("\n\nPassed div_3 testing\n");

/* test the DR reduction */
   printf("testing mp_dr_reduce...\n");
   for (cnt = 2; cnt < 32; cnt++) {
       printf("%d digit modulus\n", cnt);
       mp_grow(&a, cnt);
       mp_zero(&a);
       for (ix = 1; ix < cnt; ix++) {
           a.dp[ix] = MP_MASK;
       }
       a.used = cnt;
       a.dp[0] = 3;

       mp_rand(&b, cnt - 1);
       mp_copy(&b, &c);

      rr = 0;
      do {
         if (!(rr & 127)) { printf("%9lu\r", rr); fflush(stdout); }
         mp_sqr(&b, &b); mp_add_d(&b, 1, &b);
         mp_copy(&b, &c);

         mp_mod(&b, &a, &b);
         mp_dr_reduce(&c, &a, (((mp_digit)1)<<DIGIT_BIT)-a.dp[0]);

         if (mp_cmp(&b, &c) != MP_EQ) {
            printf("Failed on trial %lu\n", rr); exit(-1);

         }
      } while (++rr < 500);
      printf("Passed DR test for %d digits\n", cnt);
   }

#endif

   div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
   sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n = sub_d_n= 0;

   /* force KARA and TOOM to enable despite cutoffs */
   KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 110;
   TOOM_SQR_CUTOFF      = TOOM_MUL_CUTOFF      = 150;

   for (;;) {
       /* randomly clear and re-init one variable, this has the affect of triming the alloc space */
       switch (abs(rand()) % 7) {
           case 0:  mp_clear(&a); mp_init(&a); break;
           case 1:  mp_clear(&b); mp_init(&b); break;
           case 2:  mp_clear(&c); mp_init(&c); break;
           case 3:  mp_clear(&d); mp_init(&d); break;
           case 4:  mp_clear(&e); mp_init(&e); break;
           case 5:  mp_clear(&f); mp_init(&f); break;
           case 6:  break; /* don't clear any */
       }


       printf("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ", add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n, expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n);
       fgets(cmd, 4095, stdin);
       cmd[strlen(cmd)-1] = 0;
       printf("%s  ]\r",cmd); fflush(stdout);
       if (!strcmp(cmd, "mul2d")) { ++mul2d_n;
          fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64);
          fgets(buf, 4095, stdin); sscanf(buf, "%d", &rr);
          fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64);

          mp_mul_2d(&a, rr, &a);
          a.sign = b.sign;
          if (mp_cmp(&a, &b) != MP_EQ) {
             printf("mul2d failed, rr == %d\n",rr);
             draw(&a);
             draw(&b);
             return 0;
          }
       } else if (!strcmp(cmd, "div2d")) { ++div2d_n;
          fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64);
          fgets(buf, 4095, stdin); sscanf(buf, "%d", &rr);
          fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64);

          mp_div_2d(&a, rr, &a, &e);
          a.sign = b.sign;
          if (a.used == b.used && a.used == 0) { a.sign = b.sign = MP_ZPOS; }
          if (mp_cmp(&a, &b) != MP_EQ) {
             printf("div2d failed, rr == %d\n",rr);
             draw(&a);
             draw(&b);
             return 0;
          }
       } else if (!strcmp(cmd, "add")) { ++add_n;
          fgets(buf, 4095, stdin);  mp_read_radix(&a, buf, 64);
          fgets(buf, 4095, stdin);  mp_read_radix(&b, buf, 64);
          fgets(buf, 4095, stdin);  mp_read_radix(&c, buf, 64);
          mp_copy(&a, &d);
          mp_add(&d, &b, &d);
          if (mp_cmp(&c, &d) != MP_EQ) {
             printf("add %lu failure!\n", add_n);
draw(&a);draw(&b);draw(&c);draw(&d);
             return 0;
          }

          /* test the sign/unsigned storage functions */

          rr = mp_signed_bin_size(&c);
          mp_to_signed_bin(&c, (unsigned char *)cmd);
          memset(cmd+rr, rand()&255, sizeof(cmd)-rr);
          mp_read_signed_bin(&d, (unsigned char *)cmd, rr);
          if (mp_cmp(&c, &d) != MP_EQ) {
             printf("mp_signed_bin failure!\n");
             draw(&c);
             draw(&d);
             return 0;
          }


          rr = mp_unsigned_bin_size(&c);
          mp_to_unsigned_bin(&c, (unsigned char *)cmd);
          memset(cmd+rr, rand()&255, sizeof(cmd)-rr);
          mp_read_unsigned_bin(&d, (unsigned char *)cmd, rr);
          if (mp_cmp_mag(&c, &d) != MP_EQ) {
             printf("mp_unsigned_bin failure!\n");
             draw(&c);
             draw(&d);
             return 0;
          }

       } else if (!strcmp(cmd, "sub")) { ++sub_n;
          fgets(buf, 4095, stdin);  mp_read_radix(&a, buf, 64);
          fgets(buf, 4095, stdin);  mp_read_radix(&b, buf, 64);
          fgets(buf, 4095, stdin);  mp_read_radix(&c, buf, 64);
          mp_copy(&a, &d);
          mp_sub(&d, &b, &d);
          if (mp_cmp(&c, &d) != MP_EQ) {
             printf("sub %lu failure!\n", sub_n);
draw(&a);draw(&b);draw(&c);draw(&d);
             return 0;
          }
       } else if (!strcmp(cmd, "mul")) { ++mul_n;
          fgets(buf, 4095, stdin);  mp_read_radix(&a, buf, 64);
          fgets(buf, 4095, stdin);  mp_read_radix(&b, buf, 64);
          fgets(buf, 4095, stdin);  mp_read_radix(&c, buf, 64);
          mp_copy(&a, &d);
          mp_mul(&d, &b, &d);
          if (mp_cmp(&c, &d) != MP_EQ) {
             printf("mul %lu failure!\n", mul_n);
draw(&a);draw(&b);draw(&c);draw(&d);
             return 0;
          }
       } else if (!strcmp(cmd, "div")) { ++div_n;
          fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64);
          fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64);
          fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 64);
          fgets(buf, 4095, stdin); mp_read_radix(&d, buf, 64);

          mp_div(&a, &b, &e, &f);
          if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) {
             printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e), mp_cmp(&d, &f));
draw(&a);draw(&b);draw(&c);draw(&d); draw(&e); draw(&f);
             return 0;
          }

       } else if (!strcmp(cmd, "sqr")) { ++sqr_n;
          fgets(buf, 4095, stdin);  mp_read_radix(&a, buf, 64);
          fgets(buf, 4095, stdin);  mp_read_radix(&b, buf, 64);
          mp_copy(&a, &c);
          mp_sqr(&c, &c);
          if (mp_cmp(&b, &c) != MP_EQ) {
             printf("sqr %lu failure!\n", sqr_n);
draw(&a);draw(&b);draw(&c);
             return 0;
          }
       } else if (!strcmp(cmd, "gcd")) { ++gcd_n;
          fgets(buf, 4095, stdin);  mp_read_radix(&a, buf, 64);
          fgets(buf, 4095, stdin);  mp_read_radix(&b, buf, 64);
          fgets(buf, 4095, stdin);  mp_read_radix(&c, buf, 64);
          mp_copy(&a, &d);
          mp_gcd(&d, &b, &d);
          d.sign = c.sign;
          if (mp_cmp(&c, &d) != MP_EQ) {
             printf("gcd %lu failure!\n", gcd_n);
draw(&a);draw(&b);draw(&c);draw(&d);
             return 0;
          }
       } else if (!strcmp(cmd, "lcm")) { ++lcm_n;
             fgets(buf, 4095, stdin);  mp_read_radix(&a, buf, 64);
             fgets(buf, 4095, stdin);  mp_read_radix(&b, buf, 64);
             fgets(buf, 4095, stdin);  mp_read_radix(&c, buf, 64);
             mp_copy(&a, &d);
             mp_lcm(&d, &b, &d);
             d.sign = c.sign;
             if (mp_cmp(&c, &d) != MP_EQ) {
                printf("lcm %lu failure!\n", lcm_n);
   draw(&a);draw(&b);draw(&c);draw(&d);
                return 0;
             }
       } else if (!strcmp(cmd, "expt")) {  ++expt_n;
             fgets(buf, 4095, stdin);  mp_read_radix(&a, buf, 64);
             fgets(buf, 4095, stdin);  mp_read_radix(&b, buf, 64);
             fgets(buf, 4095, stdin);  mp_read_radix(&c, buf, 64);
             fgets(buf, 4095, stdin);  mp_read_radix(&d, buf, 64);
             mp_copy(&a, &e);
             mp_exptmod(&e, &b, &c, &e);
             if (mp_cmp(&d, &e) != MP_EQ) {
                printf("expt %lu failure!\n", expt_n);
   draw(&a);draw(&b);draw(&c);draw(&d); draw(&e);
                return 0;
             }
       } else if (!strcmp(cmd, "invmod")) {  ++inv_n;
             fgets(buf, 4095, stdin);  mp_read_radix(&a, buf, 64);
             fgets(buf, 4095, stdin);  mp_read_radix(&b, buf, 64);
             fgets(buf, 4095, stdin);  mp_read_radix(&c, buf, 64);
             mp_invmod(&a, &b, &d);
             mp_mulmod(&d,&a,&b,&e);
             if (mp_cmp_d(&e, 1) != MP_EQ) {
                printf("inv [wrong value from MPI?!] failure\n");
                draw(&a);draw(&b);draw(&c);draw(&d);
                mp_gcd(&a, &b, &e);
                draw(&e);
                return 0;
             }

       } else if (!strcmp(cmd, "div2")) { ++div2_n;
             fgets(buf, 4095, stdin);  mp_read_radix(&a, buf, 64);
             fgets(buf, 4095, stdin);  mp_read_radix(&b, buf, 64);
             mp_div_2(&a, &c);
             if (mp_cmp(&c, &b) != MP_EQ) {
                 printf("div_2 %lu failure\n", div2_n);
                 draw(&a);
                 draw(&b);
                 draw(&c);
                 return 0;
             }
       } else if (!strcmp(cmd, "mul2")) { ++mul2_n;
             fgets(buf, 4095, stdin);  mp_read_radix(&a, buf, 64);
             fgets(buf, 4095, stdin);  mp_read_radix(&b, buf, 64);
             mp_mul_2(&a, &c);
             if (mp_cmp(&c, &b) != MP_EQ) {
                 printf("mul_2 %lu failure\n", mul2_n);
                 draw(&a);
                 draw(&b);
                 draw(&c);
                 return 0;
             }
       } else if (!strcmp(cmd, "add_d")) { ++add_d_n;
              fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64);
              fgets(buf, 4095, stdin); sscanf(buf, "%d", &ix);
              fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64);
              mp_add_d(&a, ix, &c);
              if (mp_cmp(&b, &c) != MP_EQ) {
                 printf("add_d %lu failure\n", add_d_n);
                 draw(&a);
                 draw(&b);
                 draw(&c);
                 printf("d == %d\n", ix);
                 return 0;
              }
       } else if (!strcmp(cmd, "sub_d")) { ++sub_d_n;
              fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64);
              fgets(buf, 4095, stdin); sscanf(buf, "%d", &ix);
              fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64);
              mp_sub_d(&a, ix, &c);
              if (mp_cmp(&b, &c) != MP_EQ) {
                 printf("sub_d %lu failure\n", sub_d_n);
                 draw(&a);
                 draw(&b);
                 draw(&c);
                 printf("d == %d\n", ix);
                 return 0;
              }
       }
   }
   return 0;
}
Example #7
0
/**
  Sign a hash with DSA
  @param in       The hash to sign
  @param inlen    The length of the hash to sign
  @param r        The "r" integer of the signature (caller must initialize with mp_init() first)
  @param s        The "s" integer of the signature (caller must initialize with mp_init() first)
  @param prng     An active PRNG state
  @param wprng    The index of the PRNG desired
  @param key      A private DSA key
  @return CRYPT_OK if successful
*/
int dsa_sign_hash_raw(const unsigned char *in,  unsigned long inlen,
                                   void   *r,   void *s,
                               prng_state *prng, int wprng, dsa_key *key)
{
   void         *k, *kinv, *tmp;
   unsigned char *buf;
   int            err, qbits;

   LTC_ARGCHK(in  != NULL);
   LTC_ARGCHK(r   != NULL);
   LTC_ARGCHK(s   != NULL);
   LTC_ARGCHK(key != NULL);

   if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
      return err;
   }
   if (key->type != PK_PRIVATE) {
      return CRYPT_PK_NOT_PRIVATE;
   }

   /* check group order size  */
   if (key->qord >= LTC_MDSA_MAX_GROUP) {
      return CRYPT_INVALID_ARG;
   }

   buf = XMALLOC(LTC_MDSA_MAX_GROUP);
   if (buf == NULL) {
      return CRYPT_MEM;
   }

   /* Init our temps */
   if ((err = mp_init_multi(&k, &kinv, &tmp, NULL)) != CRYPT_OK)                       { goto ERRBUF; }

   qbits = mp_count_bits(key->q);
retry:

   do {
      /* gen random k */
      if ((err = rand_bn_bits(k, qbits, prng, wprng)) != CRYPT_OK)                     { goto error; }

      /* k should be from range: 1 <= k <= q-1 (see FIPS 186-4 B.2.2) */
      if (mp_cmp_d(k, 0) != LTC_MP_GT || mp_cmp(k, key->q) != LTC_MP_LT)               { goto retry; }

      /* test gcd */
      if ((err = mp_gcd(k, key->q, tmp)) != CRYPT_OK)                                  { goto error; }
   } while (mp_cmp_d(tmp, 1) != LTC_MP_EQ);

   /* now find 1/k mod q */
   if ((err = mp_invmod(k, key->q, kinv)) != CRYPT_OK)                                 { goto error; }

   /* now find r = g^k mod p mod q */
   if ((err = mp_exptmod(key->g, k, key->p, r)) != CRYPT_OK)                           { goto error; }
   if ((err = mp_mod(r, key->q, r)) != CRYPT_OK)                                       { goto error; }

   if (mp_iszero(r) == LTC_MP_YES)                                                     { goto retry; }

   /* FIPS 186-4 4.6: use leftmost min(bitlen(q), bitlen(hash)) bits of 'hash'*/
   inlen = MIN(inlen, (unsigned long)(key->qord));

   /* now find s = (in + xr)/k mod q */
   if ((err = mp_read_unsigned_bin(tmp, (unsigned char *)in, inlen)) != CRYPT_OK)      { goto error; }
   if ((err = mp_mul(key->x, r, s)) != CRYPT_OK)                                       { goto error; }
   if ((err = mp_add(s, tmp, s)) != CRYPT_OK)                                          { goto error; }
   if ((err = mp_mulmod(s, kinv, key->q, s)) != CRYPT_OK)                              { goto error; }

   if (mp_iszero(s) == LTC_MP_YES)                                                     { goto retry; }

   err = CRYPT_OK;
error:
   mp_clear_multi(k, kinv, tmp, NULL);
ERRBUF:
#ifdef LTC_CLEAN_STACK
   zeromem(buf, LTC_MDSA_MAX_GROUP);
#endif
   XFREE(buf);
   return err;
}
int ecc_sign_hash(const unsigned char *in,  unsigned long inlen, 
                        unsigned char *out, unsigned long *outlen, 
                        prng_state *prng, int wprng, ecc_key *key)
{
   ecc_key       pubkey;
   void          *r, *s, *e, *p;
   int           err;

   LTC_ARGCHK(in     != NULL);
   LTC_ARGCHK(out    != NULL);
   LTC_ARGCHK(outlen != NULL);
   LTC_ARGCHK(key    != NULL);

   /* is this a private key? */
   if (key->type != PK_PRIVATE) {
      return CRYPT_PK_NOT_PRIVATE;
   }
   
   /* is the IDX valid ?  */
   if (ltc_ecc_is_valid_idx(key->idx) != 1) {
      return CRYPT_PK_INVALID_TYPE;
   }
   
   if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
      return err;
   }

   /* get the hash and load it as a bignum into 'e' */
   /* init the bignums */
   if ((err = mp_init_multi(&r, &s, &p, &e, NULL)) != CRYPT_OK) { 
      return err;
   }
   if ((err = mp_read_radix(p, (char *)key->dp->order, 16)) != CRYPT_OK)                      { goto errnokey; }
   if ((err = mp_read_unsigned_bin(e, (unsigned char *)in, (int)inlen)) != CRYPT_OK)          { goto errnokey; }

   /* make up a key and export the public copy */
   for (;;) {
      if ((err = ecc_make_key_ex(prng, wprng, &pubkey, key->dp)) != CRYPT_OK) {
         goto errnokey;
      }

      /* find r = x1 mod n */
      if ((err = mp_mod(pubkey.pubkey.x, p, r)) != CRYPT_OK)                 { goto error; }

      if (mp_iszero(r) == LTC_MP_YES) {
         ecc_free(&pubkey);
      } else { 
        /* find s = (e + xr)/k */
        if ((err = mp_invmod(pubkey.k, p, pubkey.k)) != CRYPT_OK)            { goto error; } /* k = 1/k */
        if ((err = mp_mulmod(key->k, r, p, s)) != CRYPT_OK)                  { goto error; } /* s = xr */
        if ((err = mp_add(e, s, s)) != CRYPT_OK)                             { goto error; } /* s = e +  xr */
        if ((err = mp_mod(s, p, s)) != CRYPT_OK)                             { goto error; } /* s = e +  xr */
        if ((err = mp_mulmod(s, pubkey.k, p, s)) != CRYPT_OK)                { goto error; } /* s = (e + xr)/k */
        ecc_free(&pubkey);
        if (mp_iszero(s) == LTC_MP_NO) {
           break;
        }
      }
   }

   /* store as SEQUENCE { r, s -- integer } */
   err = der_encode_sequence_multi(out, outlen,
                             LTC_ASN1_INTEGER, 1UL, r,
                             LTC_ASN1_INTEGER, 1UL, s,
                             LTC_ASN1_EOL, 0UL, NULL);
   goto errnokey;
error:
   ecc_free(&pubkey);
errnokey:
   mp_clear_multi(r, s, p, e, NULL);
   return err;   
}
Example #9
0
File: demo.c Project: mkj/dropbear
int main(void)
{
   unsigned rr;
   int cnt, ix;
#if LTM_DEMO_TEST_VS_MTEST
   unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n,
      gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n;
   char* ret;
#else
   unsigned long s, t;
   unsigned long long q, r;
   mp_digit mp;
   int i, n, err, should;
#endif

   if (mp_init_multi(&a, &b, &c, &d, &e, &f, NULL)!= MP_OKAY)
     return EXIT_FAILURE;

   atexit(_cleanup);

#if defined(LTM_DEMO_REAL_RAND)
   if (!fd_urandom) {
      fd_urandom = fopen("/dev/urandom", "r");
      if (!fd_urandom) {
#if !defined(_WIN32)
         fprintf(stderr, "\ncould not open /dev/urandom\n");
#endif
      }
   }
#endif
   srand(LTM_DEMO_RAND_SEED);

#ifdef MP_8BIT
   printf("Digit size 8 Bit \n");
#endif
#ifdef MP_16BIT
   printf("Digit size 16 Bit \n");
#endif
#ifdef MP_32BIT
   printf("Digit size 32 Bit \n");
#endif
#ifdef MP_64BIT
   printf("Digit size 64 Bit \n");
#endif
   printf("Size of mp_digit: %u\n", (unsigned int)sizeof(mp_digit));
   printf("Size of mp_word: %u\n", (unsigned int)sizeof(mp_word));
   printf("DIGIT_BIT: %d\n", DIGIT_BIT);
   printf("MP_PREC: %d\n", MP_PREC);

#if LTM_DEMO_TEST_VS_MTEST == 0
   // trivial stuff
   // a: 0->5
   mp_set_int(&a, 5);
   // a: 5-> b: -5
   mp_neg(&a, &b);
   if (mp_cmp(&a, &b) != MP_GT) {
      return EXIT_FAILURE;
   }
   if (mp_cmp(&b, &a) != MP_LT) {
      return EXIT_FAILURE;
   }
   // a: 5-> a: -5
   mp_neg(&a, &a);
   if (mp_cmp(&b, &a) != MP_EQ) {
      return EXIT_FAILURE;
   }
   // a: -5-> b: 5
   mp_abs(&a, &b);
   if (mp_isneg(&b) != MP_NO) {
      return EXIT_FAILURE;
   }
   // a: -5-> b: -4
   mp_add_d(&a, 1, &b);
   if (mp_isneg(&b) != MP_YES) {
      return EXIT_FAILURE;
   }
   if (mp_get_int(&b) != 4) {
      return EXIT_FAILURE;
   }
   // a: -5-> b: 1
   mp_add_d(&a, 6, &b);
   if (mp_get_int(&b) != 1) {
      return EXIT_FAILURE;
   }
   // a: -5-> a: 1
   mp_add_d(&a, 6, &a);
   if (mp_get_int(&a) != 1) {
      return EXIT_FAILURE;
   }
   mp_zero(&a);
   // a: 0-> a: 6
   mp_add_d(&a, 6, &a);
   if (mp_get_int(&a) != 6) {
      return EXIT_FAILURE;
   }


   mp_set_int(&a, 0);
   mp_set_int(&b, 1);
   if ((err = mp_jacobi(&a, &b, &i)) != MP_OKAY) {
      printf("Failed executing mp_jacobi(0 | 1) %s.\n", mp_error_to_string(err));
      return EXIT_FAILURE;
   }
   if (i != 1) {
      printf("Failed trivial mp_jacobi(0 | 1) %d != 1\n", i);
      return EXIT_FAILURE;
   }
   for (cnt = 0; cnt < (int)(sizeof(jacobi)/sizeof(jacobi[0])); ++cnt) {
      mp_set_int(&b, jacobi[cnt].n);
      /* only test positive values of a */
      for (n = -5; n <= 10; ++n) {
         mp_set_int(&a, abs(n));
         should = MP_OKAY;
         if (n < 0) {
            mp_neg(&a, &a);
            /* Until #44 is fixed the negative a's must fail */
            should = MP_VAL;
         }
         if ((err = mp_jacobi(&a, &b, &i)) != should) {
            printf("Failed executing mp_jacobi(%d | %lu) %s.\n", n, jacobi[cnt].n, mp_error_to_string(err));
            return EXIT_FAILURE;
         }
         if (err == MP_OKAY && i != jacobi[cnt].c[n + 5]) {
            printf("Failed trivial mp_jacobi(%d | %lu) %d != %d\n", n, jacobi[cnt].n, i, jacobi[cnt].c[n + 5]);
            return EXIT_FAILURE;
         }
      }
   }

   // test mp_get_int
   printf("\n\nTesting: mp_get_int");
   for (i = 0; i < 1000; ++i) {
      t = ((unsigned long) rand () * rand () + 1) & 0xFFFFFFFF;
      mp_set_int (&a, t);
      if (t != mp_get_int (&a)) {
         printf ("\nmp_get_int() bad result!");
         return EXIT_FAILURE;
      }
   }
   mp_set_int(&a, 0);
   if (mp_get_int(&a) != 0) {
      printf("\nmp_get_int() bad result!");
      return EXIT_FAILURE;
   }
   mp_set_int(&a, 0xffffffff);
   if (mp_get_int(&a) != 0xffffffff) {
      printf("\nmp_get_int() bad result!");
      return EXIT_FAILURE;
   }

   printf("\n\nTesting: mp_get_long\n");
   for (i = 0; i < (int)(sizeof(unsigned long)*CHAR_BIT) - 1; ++i) {
      t = (1ULL << (i+1)) - 1;
      if (!t)
         t = -1;
      printf(" t = 0x%lx i = %d\r", t, i);
      do {
         if (mp_set_long(&a, t) != MP_OKAY) {
            printf("\nmp_set_long() error!");
            return EXIT_FAILURE;
         }
         s = mp_get_long(&a);
         if (s != t) {
            printf("\nmp_get_long() bad result! 0x%lx != 0x%lx", s, t);
            return EXIT_FAILURE;
         }
         t <<= 1;
      } while(t);
   }

   printf("\n\nTesting: mp_get_long_long\n");
   for (i = 0; i < (int)(sizeof(unsigned long long)*CHAR_BIT) - 1; ++i) {
      r = (1ULL << (i+1)) - 1;
      if (!r)
         r = -1;
      printf(" r = 0x%llx i = %d\r", r, i);
      do {
         if (mp_set_long_long(&a, r) != MP_OKAY) {
            printf("\nmp_set_long_long() error!");
            return EXIT_FAILURE;
         }
         q = mp_get_long_long(&a);
         if (q != r) {
            printf("\nmp_get_long_long() bad result! 0x%llx != 0x%llx", q, r);
            return EXIT_FAILURE;
         }
         r <<= 1;
      } while(r);
   }

   // test mp_sqrt
   printf("\n\nTesting: mp_sqrt\n");
   for (i = 0; i < 1000; ++i) {
      printf ("%6d\r", i);
      fflush (stdout);
      n = (rand () & 15) + 1;
      mp_rand (&a, n);
      if (mp_sqrt (&a, &b) != MP_OKAY) {
         printf ("\nmp_sqrt() error!");
         return EXIT_FAILURE;
      }
      mp_n_root_ex (&a, 2, &c, 0);
      mp_n_root_ex (&a, 2, &d, 1);
      if (mp_cmp_mag (&c, &d) != MP_EQ) {
         printf ("\nmp_n_root_ex() bad result!");
         return EXIT_FAILURE;
      }
      if (mp_cmp_mag (&b, &c) != MP_EQ) {
         printf ("mp_sqrt() bad result!\n");
         return EXIT_FAILURE;
      }
   }

   printf("\n\nTesting: mp_is_square\n");
   for (i = 0; i < 1000; ++i) {
      printf ("%6d\r", i);
      fflush (stdout);

      /* test mp_is_square false negatives */
      n = (rand () & 7) + 1;
      mp_rand (&a, n);
      mp_sqr (&a, &a);
      if (mp_is_square (&a, &n) != MP_OKAY) {
         printf ("\nfn:mp_is_square() error!");
         return EXIT_FAILURE;
      }
      if (n == 0) {
         printf ("\nfn:mp_is_square() bad result!");
         return EXIT_FAILURE;
      }

      /* test for false positives */
      mp_add_d (&a, 1, &a);
      if (mp_is_square (&a, &n) != MP_OKAY) {
         printf ("\nfp:mp_is_square() error!");
         return EXIT_FAILURE;
      }
      if (n == 1) {
         printf ("\nfp:mp_is_square() bad result!");
         return EXIT_FAILURE;
      }

   }
   printf("\n\n");

   // r^2 = n (mod p)
   for (i = 0; i < (int)(sizeof(sqrtmod_prime)/sizeof(sqrtmod_prime[0])); ++i) {
      mp_set_int(&a, sqrtmod_prime[i].p);
      mp_set_int(&b, sqrtmod_prime[i].n);
      if (mp_sqrtmod_prime(&b, &a, &c) != MP_OKAY) {
         printf("Failed executing %d. mp_sqrtmod_prime\n", (i+1));
         return EXIT_FAILURE;
      }
      if (mp_cmp_d(&c, sqrtmod_prime[i].r) != MP_EQ) {
         printf("Failed %d. trivial mp_sqrtmod_prime\n", (i+1));
         ndraw(&c, "r");
         return EXIT_FAILURE;
      }
   }

   /* test for size */
   for (ix = 10; ix < 128; ix++) {
      printf ("Testing (not safe-prime): %9d bits    \r", ix);
      fflush (stdout);
      err = mp_prime_random_ex (&a, 8, ix,
                                (rand () & 1) ? 0 : LTM_PRIME_2MSB_ON, myrng,
                                NULL);
      if (err != MP_OKAY) {
         printf ("failed with err code %d\n", err);
         return EXIT_FAILURE;
      }
      if (mp_count_bits (&a) != ix) {
         printf ("Prime is %d not %d bits!!!\n", mp_count_bits (&a), ix);
         return EXIT_FAILURE;
      }
   }
   printf("\n");

   for (ix = 16; ix < 128; ix++) {
      printf ("Testing (    safe-prime): %9d bits    \r", ix);
      fflush (stdout);
      err = mp_prime_random_ex (
            &a, 8, ix, ((rand () & 1) ? 0 : LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE,
            myrng, NULL);
      if (err != MP_OKAY) {
         printf ("failed with err code %d\n", err);
         return EXIT_FAILURE;
      }
      if (mp_count_bits (&a) != ix) {
         printf ("Prime is %d not %d bits!!!\n", mp_count_bits (&a), ix);
         return EXIT_FAILURE;
      }
      /* let's see if it's really a safe prime */
      mp_sub_d (&a, 1, &a);
      mp_div_2 (&a, &a);
      mp_prime_is_prime (&a, 8, &cnt);
      if (cnt != MP_YES) {
         printf ("sub is not prime!\n");
         return EXIT_FAILURE;
      }
   }

   printf("\n\n");

   // test montgomery
   printf("Testing: montgomery...\n");
   for (i = 1; i <= 10; i++) {
      if (i == 10)
         i = 1000;
      printf(" digit size: %2d\r", i);
      fflush(stdout);
      for (n = 0; n < 1000; n++) {
         mp_rand(&a, i);
         a.dp[0] |= 1;

         // let's see if R is right
         mp_montgomery_calc_normalization(&b, &a);
         mp_montgomery_setup(&a, &mp);

         // now test a random reduction
         for (ix = 0; ix < 100; ix++) {
             mp_rand(&c, 1 + abs(rand()) % (2*i));
             mp_copy(&c, &d);
             mp_copy(&c, &e);

             mp_mod(&d, &a, &d);
             mp_montgomery_reduce(&c, &a, mp);
             mp_mulmod(&c, &b, &a, &c);

             if (mp_cmp(&c, &d) != MP_EQ) {
printf("d = e mod a, c = e MOD a\n");
mp_todecimal(&a, buf); printf("a = %s\n", buf);
mp_todecimal(&e, buf); printf("e = %s\n", buf);
mp_todecimal(&d, buf); printf("d = %s\n", buf);
mp_todecimal(&c, buf); printf("c = %s\n", buf);
printf("compare no compare!\n"); return EXIT_FAILURE; }
             /* only one big montgomery reduction */
             if (i > 10)
             {
                n = 1000;
                ix = 100;
             }
         }
      }
   }

   printf("\n\n");

   mp_read_radix(&a, "123456", 10);
   mp_toradix_n(&a, buf, 10, 3);
   printf("a == %s\n", buf);
   mp_toradix_n(&a, buf, 10, 4);
   printf("a == %s\n", buf);
   mp_toradix_n(&a, buf, 10, 30);
   printf("a == %s\n", buf);


#if 0
   for (;;) {
      fgets(buf, sizeof(buf), stdin);
      mp_read_radix(&a, buf, 10);
      mp_prime_next_prime(&a, 5, 1);
      mp_toradix(&a, buf, 10);
      printf("%s, %lu\n", buf, a.dp[0] & 3);
   }
#endif

   /* test mp_cnt_lsb */
   printf("\n\nTesting: mp_cnt_lsb");
   mp_set(&a, 1);
   for (ix = 0; ix < 1024; ix++) {
      if (mp_cnt_lsb (&a) != ix) {
         printf ("Failed at %d, %d\n", ix, mp_cnt_lsb (&a));
         return EXIT_FAILURE;
      }
      mp_mul_2 (&a, &a);
   }

/* test mp_reduce_2k */
   printf("\n\nTesting: mp_reduce_2k\n");
   for (cnt = 3; cnt <= 128; ++cnt) {
      mp_digit tmp;

      mp_2expt (&a, cnt);
      mp_sub_d (&a, 2, &a); /* a = 2**cnt - 2 */

      printf ("\r %4d bits", cnt);
      printf ("(%d)", mp_reduce_is_2k (&a));
      mp_reduce_2k_setup (&a, &tmp);
      printf ("(%lu)", (unsigned long) tmp);
      for (ix = 0; ix < 1000; ix++) {
         if (!(ix & 127)) {
            printf (".");
            fflush (stdout);
         }
         mp_rand (&b, (cnt / DIGIT_BIT + 1) * 2);
         mp_copy (&c, &b);
         mp_mod (&c, &a, &c);
         mp_reduce_2k (&b, &a, 2);
         if (mp_cmp (&c, &b)) {
            printf ("FAILED\n");
            return EXIT_FAILURE;
         }
      }
   }

/* test mp_div_3  */
   printf("\n\nTesting: mp_div_3...\n");
   mp_set(&d, 3);
   for (cnt = 0; cnt < 10000;) {
      mp_digit r2;

      if (!(++cnt & 127))
      {
        printf("%9d\r", cnt);
        fflush(stdout);
      }
      mp_rand(&a, abs(rand()) % 128 + 1);
      mp_div(&a, &d, &b, &e);
      mp_div_3(&a, &c, &r2);

      if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) {
	 printf("\nmp_div_3 => Failure\n");
      }
   }
   printf("\nPassed div_3 testing");

/* test the DR reduction */
   printf("\n\nTesting: mp_dr_reduce...\n");
   for (cnt = 2; cnt < 32; cnt++) {
      printf ("\r%d digit modulus", cnt);
      mp_grow (&a, cnt);
      mp_zero (&a);
      for (ix = 1; ix < cnt; ix++) {
         a.dp[ix] = MP_MASK;
      }
      a.used = cnt;
      a.dp[0] = 3;

      mp_rand (&b, cnt - 1);
      mp_copy (&b, &c);

      rr = 0;
      do {
         if (!(rr & 127)) {
            printf (".");
            fflush (stdout);
         }
         mp_sqr (&b, &b);
         mp_add_d (&b, 1, &b);
         mp_copy (&b, &c);

         mp_mod (&b, &a, &b);
         mp_dr_setup(&a, &mp),
         mp_dr_reduce (&c, &a, mp);

         if (mp_cmp (&b, &c) != MP_EQ) {
            printf ("Failed on trial %u\n", rr);
            return EXIT_FAILURE;
         }
      } while (++rr < 500);
      printf (" passed");
      fflush (stdout);
   }

#if LTM_DEMO_TEST_REDUCE_2K_L
/* test the mp_reduce_2k_l code */
#if LTM_DEMO_TEST_REDUCE_2K_L == 1
/* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */
   mp_2expt(&a, 1024);
   mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16);
   mp_sub(&a, &b, &a);
#elif LTM_DEMO_TEST_REDUCE_2K_L == 2
/*  p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F  */
   mp_2expt(&a, 2048);
   mp_read_radix(&b,
		 "1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F",
		 16);
   mp_sub(&a, &b, &a);
#else
#error oops
#endif

   mp_todecimal(&a, buf);
   printf("\n\np==%s\n", buf);
/* now mp_reduce_is_2k_l() should return */
   if (mp_reduce_is_2k_l(&a) != 1) {
      printf("mp_reduce_is_2k_l() return 0, should be 1\n");
      return EXIT_FAILURE;
   }
   mp_reduce_2k_setup_l(&a, &d);
   /* now do a million square+1 to see if it varies */
   mp_rand(&b, 64);
   mp_mod(&b, &a, &b);
   mp_copy(&b, &c);
   printf("Testing: mp_reduce_2k_l...");
   fflush(stdout);
   for (cnt = 0; cnt < (int)(1UL << 20); cnt++) {
      mp_sqr(&b, &b);
      mp_add_d(&b, 1, &b);
      mp_reduce_2k_l(&b, &a, &d);
      mp_sqr(&c, &c);
      mp_add_d(&c, 1, &c);
      mp_mod(&c, &a, &c);
      if (mp_cmp(&b, &c) != MP_EQ) {
	 printf("mp_reduce_2k_l() failed at step %d\n", cnt);
	 mp_tohex(&b, buf);
	 printf("b == %s\n", buf);
	 mp_tohex(&c, buf);
	 printf("c == %s\n", buf);
	 return EXIT_FAILURE;
      }
   }
   printf("...Passed\n");
#endif /* LTM_DEMO_TEST_REDUCE_2K_L */

#else

   div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
      sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n =
      sub_d_n = 0;

   /* force KARA and TOOM to enable despite cutoffs */
   KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8;
   TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16;

   for (;;) {
      /* randomly clear and re-init one variable, this has the affect of triming the alloc space */
      switch (abs(rand()) % 7) {
      case 0:
	 mp_clear(&a);
	 mp_init(&a);
	 break;
      case 1:
	 mp_clear(&b);
	 mp_init(&b);
	 break;
      case 2:
	 mp_clear(&c);
	 mp_init(&c);
	 break;
      case 3:
	 mp_clear(&d);
	 mp_init(&d);
	 break;
      case 4:
	 mp_clear(&e);
	 mp_init(&e);
	 break;
      case 5:
	 mp_clear(&f);
	 mp_init(&f);
	 break;
      case 6:
	 break;			/* don't clear any */
      }


      printf
	 ("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ",
	  add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n,
	  expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n);
      ret=fgets(cmd, 4095, stdin); if(!ret){_panic(__LINE__);}
      cmd[strlen(cmd) - 1] = 0;
      printf("%-6s ]\r", cmd);
      fflush(stdout);
      if (!strcmp(cmd, "mul2d")) {
	 ++mul2d_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 sscanf(buf, "%d", &rr);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);

	 mp_mul_2d(&a, rr, &a);
	 a.sign = b.sign;
	 if (mp_cmp(&a, &b) != MP_EQ) {
	    printf("mul2d failed, rr == %d\n", rr);
	    draw(&a);
	    draw(&b);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "div2d")) {
	 ++div2d_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 sscanf(buf, "%d", &rr);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);

	 mp_div_2d(&a, rr, &a, &e);
	 a.sign = b.sign;
	 if (a.used == b.used && a.used == 0) {
	    a.sign = b.sign = MP_ZPOS;
	 }
	 if (mp_cmp(&a, &b) != MP_EQ) {
	    printf("div2d failed, rr == %d\n", rr);
	    draw(&a);
	    draw(&b);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "add")) {
	 ++add_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_add(&d, &b, &d);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("add %lu failure!\n", add_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }

	 /* test the sign/unsigned storage functions */

	 rr = mp_signed_bin_size(&c);
	 mp_to_signed_bin(&c, (unsigned char *) cmd);
	 memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
	 mp_read_signed_bin(&d, (unsigned char *) cmd, rr);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("mp_signed_bin failure!\n");
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }


	 rr = mp_unsigned_bin_size(&c);
	 mp_to_unsigned_bin(&c, (unsigned char *) cmd);
	 memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
	 mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr);
	 if (mp_cmp_mag(&c, &d) != MP_EQ) {
	    printf("mp_unsigned_bin failure!\n");
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }

      } else if (!strcmp(cmd, "sub")) {
	 ++sub_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_sub(&d, &b, &d);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("sub %lu failure!\n", sub_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "mul")) {
	 ++mul_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_mul(&d, &b, &d);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("mul %lu failure!\n", mul_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "div")) {
	 ++div_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&d, buf, 64);

	 mp_div(&a, &b, &e, &f);
	 if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) {
	    printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e),
		   mp_cmp(&d, &f));
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    draw(&e);
	    draw(&f);
	    return EXIT_FAILURE;
	 }

      } else if (!strcmp(cmd, "sqr")) {
	 ++sqr_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 mp_copy(&a, &c);
	 mp_sqr(&c, &c);
	 if (mp_cmp(&b, &c) != MP_EQ) {
	    printf("sqr %lu failure!\n", sqr_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "gcd")) {
	 ++gcd_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_gcd(&d, &b, &d);
	 d.sign = c.sign;
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("gcd %lu failure!\n", gcd_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "lcm")) {
	 ++lcm_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_lcm(&d, &b, &d);
	 d.sign = c.sign;
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("lcm %lu failure!\n", lcm_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "expt")) {
	 ++expt_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&d, buf, 64);
	 mp_copy(&a, &e);
	 mp_exptmod(&e, &b, &c, &e);
	 if (mp_cmp(&d, &e) != MP_EQ) {
	    printf("expt %lu failure!\n", expt_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    draw(&e);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "invmod")) {
	 ++inv_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_invmod(&a, &b, &d);
	 mp_mulmod(&d, &a, &b, &e);
	 if (mp_cmp_d(&e, 1) != MP_EQ) {
	    printf("inv [wrong value from MPI?!] failure\n");
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    draw(&e);
	    mp_gcd(&a, &b, &e);
	    draw(&e);
	    return EXIT_FAILURE;
	 }

      } else if (!strcmp(cmd, "div2")) {
	 ++div2_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 mp_div_2(&a, &c);
	 if (mp_cmp(&c, &b) != MP_EQ) {
	    printf("div_2 %lu failure\n", div2_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "mul2")) {
	 ++mul2_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 mp_mul_2(&a, &c);
	 if (mp_cmp(&c, &b) != MP_EQ) {
	    printf("mul_2 %lu failure\n", mul2_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "add_d")) {
	 ++add_d_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 sscanf(buf, "%d", &ix);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 mp_add_d(&a, ix, &c);
	 if (mp_cmp(&b, &c) != MP_EQ) {
	    printf("add_d %lu failure\n", add_d_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    printf("d == %d\n", ix);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "sub_d")) {
	 ++sub_d_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 sscanf(buf, "%d", &ix);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 mp_sub_d(&a, ix, &c);
	 if (mp_cmp(&b, &c) != MP_EQ) {
	    printf("sub_d %lu failure\n", sub_d_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    printf("d == %d\n", ix);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "exit")) {
         printf("\nokay, exiting now\n");
         break;
      }
   }
#endif
   return 0;
}
Example #10
0
int mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode)
{
   mp_int  M[TAB_SIZE], res;
   mp_digit buf, mp;
   int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;

   /* use a pointer to the reduction algorithm.  This allows us to use
    * one of many reduction algorithms without modding the guts of
    * the code with if statements everywhere.
    */
   int (*redux)(mp_int *x, const mp_int *n, mp_digit rho);

   /* find window size */
   x = mp_count_bits(X);
   if (x <= 7) {
      winsize = 2;
   } else if (x <= 36) {
      winsize = 3;
   } else if (x <= 140) {
      winsize = 4;
   } else if (x <= 450) {
      winsize = 5;
   } else if (x <= 1303) {
      winsize = 6;
   } else if (x <= 3529) {
      winsize = 7;
   } else {
      winsize = 8;
   }

#ifdef MP_LOW_MEM
   if (winsize > 5) {
      winsize = 5;
   }
#endif

   /* init M array */
   /* init first cell */
   if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) {
      return err;
   }

   /* now init the second half of the array */
   for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
      if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) {
         for (y = 1<<(winsize-1); y < x; y++) {
            mp_clear(&M[y]);
         }
         mp_clear(&M[1]);
         return err;
      }
   }

   /* determine and setup reduction code */
   if (redmode == 0) {
#ifdef BN_MP_MONTGOMERY_SETUP_C
      /* now setup montgomery  */
      if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) {
         goto LBL_M;
      }
#else
      err = MP_VAL;
      goto LBL_M;
#endif

      /* automatically pick the comba one if available (saves quite a few calls/ifs) */
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
      if ((((P->used * 2) + 1) < (int)MP_WARRAY) &&
          (P->used < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
         redux = fast_mp_montgomery_reduce;
      } else
#endif
      {
#ifdef BN_MP_MONTGOMERY_REDUCE_C
         /* use slower baseline Montgomery method */
         redux = mp_montgomery_reduce;
#else
         err = MP_VAL;
         goto LBL_M;
#endif
      }
   } else if (redmode == 1) {
#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
      /* setup DR reduction for moduli of the form B**k - b */
      mp_dr_setup(P, &mp);
      redux = mp_dr_reduce;
#else
      err = MP_VAL;
      goto LBL_M;
#endif
   } else {
#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
      /* setup DR reduction for moduli of the form 2**k - b */
      if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
         goto LBL_M;
      }
      redux = mp_reduce_2k;
#else
      err = MP_VAL;
      goto LBL_M;
#endif
   }

   /* setup result */
   if ((err = mp_init_size(&res, P->alloc)) != MP_OKAY) {
      goto LBL_M;
   }

   /* create M table
    *

    *
    * The first half of the table is not computed though accept for M[0] and M[1]
    */

   if (redmode == 0) {
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
      /* now we need R mod m */
      if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) {
         goto LBL_RES;
      }

      /* now set M[1] to G * R mod m */
      if ((err = mp_mulmod(G, &res, P, &M[1])) != MP_OKAY) {
         goto LBL_RES;
      }
#else
      err = MP_VAL;
      goto LBL_RES;
#endif
   } else {
      mp_set(&res, 1uL);
      if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
         goto LBL_RES;
      }
   }

   /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
   if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) {
      goto LBL_RES;
   }

   for (x = 0; x < (winsize - 1); x++) {
      if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) {
         goto LBL_RES;
      }
      if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, mp)) != MP_OKAY) {
         goto LBL_RES;
      }
   }

   /* create upper table */
   for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
      if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
         goto LBL_RES;
      }
      if ((err = redux(&M[x], P, mp)) != MP_OKAY) {
         goto LBL_RES;
      }
   }

   /* set initial mode and bit cnt */
   mode   = 0;
   bitcnt = 1;
   buf    = 0;
   digidx = X->used - 1;
   bitcpy = 0;
   bitbuf = 0;

   for (;;) {
      /* grab next digit as required */
      if (--bitcnt == 0) {
         /* if digidx == -1 we are out of digits so break */
         if (digidx == -1) {
            break;
         }
         /* read next digit and reset bitcnt */
         buf    = X->dp[digidx--];
         bitcnt = (int)DIGIT_BIT;
      }

      /* grab the next msb from the exponent */
      y     = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
      buf <<= (mp_digit)1;

      /* if the bit is zero and mode == 0 then we ignore it
       * These represent the leading zero bits before the first 1 bit
       * in the exponent.  Technically this opt is not required but it
       * does lower the # of trivial squaring/reductions used
       */
      if ((mode == 0) && (y == 0)) {
         continue;
      }

      /* if the bit is zero and mode == 1 then we square */
      if ((mode == 1) && (y == 0)) {
         if ((err = mp_sqr(&res, &res)) != MP_OKAY) {
            goto LBL_RES;
         }
         if ((err = redux(&res, P, mp)) != MP_OKAY) {
            goto LBL_RES;
         }
         continue;
      }

      /* else we add it to the window */
      bitbuf |= (y << (winsize - ++bitcpy));
      mode    = 2;

      if (bitcpy == winsize) {
         /* ok window is filled so square as required and multiply  */
         /* square first */
         for (x = 0; x < winsize; x++) {
            if ((err = mp_sqr(&res, &res)) != MP_OKAY) {
               goto LBL_RES;
            }
            if ((err = redux(&res, P, mp)) != MP_OKAY) {
               goto LBL_RES;
            }
         }

         /* then multiply */
         if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) {
            goto LBL_RES;
         }
         if ((err = redux(&res, P, mp)) != MP_OKAY) {
            goto LBL_RES;
         }

         /* empty window and reset */
         bitcpy = 0;
         bitbuf = 0;
         mode   = 1;
      }
   }

   /* if bits remain then square/multiply */
   if ((mode == 2) && (bitcpy > 0)) {
      /* square then multiply if the bit is set */
      for (x = 0; x < bitcpy; x++) {
         if ((err = mp_sqr(&res, &res)) != MP_OKAY) {
            goto LBL_RES;
         }
         if ((err = redux(&res, P, mp)) != MP_OKAY) {
            goto LBL_RES;
         }

         /* get next bit of the window */
         bitbuf <<= 1;
         if ((bitbuf & (1 << winsize)) != 0) {
            /* then multiply */
            if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) {
               goto LBL_RES;
            }
            if ((err = redux(&res, P, mp)) != MP_OKAY) {
               goto LBL_RES;
            }
         }
      }
   }

   if (redmode == 0) {
      /* fixup result if Montgomery reduction is used
       * recall that any value in a Montgomery system is
       * actually multiplied by R mod n.  So we have
       * to reduce one more time to cancel out the factor
       * of R.
       */
      if ((err = redux(&res, P, mp)) != MP_OKAY) {
         goto LBL_RES;
      }
   }

   /* swap res with Y */
   mp_exch(&res, Y);
   err = MP_OKAY;
LBL_RES:
   mp_clear(&res);
LBL_M:
   mp_clear(&M[1]);
   for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
      mp_clear(&M[x]);
   }
   return err;
}
/* Store non-zero to ret if arg is square, and zero if not */
int mp_is_square(mp_int *arg,int *ret) 
{
  int           res;
  mp_digit      c;
  mp_int        t;
  unsigned long r;

  /* Default to Non-square :) */
  *ret = MP_NO; 

  if (arg->sign == MP_NEG) {
    return MP_VAL;
  }

  /* digits used?  (TSD) */
  if (arg->used == 0) {
     return MP_OKAY;
  }

  /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
  if (rem_128[127 & DIGIT(arg,0)] == 1) {
     return MP_OKAY;
  }

  /* Next check mod 105 (3*5*7) */
  if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
     return res;
  }
  if (rem_105[c] == 1) {
     return MP_OKAY;
  }


  if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
     return res;
  }
  if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
     goto ERR;
  }
  r = mp_get_int(&t);
  /* Check for other prime modules, note it's not an ERROR but we must
   * free "t" so the easiest way is to goto ERR.  We know that res
   * is already equal to MP_OKAY from the mp_mod call 
   */ 
  if ( (1L<<(r%11)) & 0x5C4L )             goto ERR;
  if ( (1L<<(r%13)) & 0x9E4L )             goto ERR;
  if ( (1L<<(r%17)) & 0x5CE8L )            goto ERR;
  if ( (1L<<(r%19)) & 0x4F50CL )           goto ERR;
  if ( (1L<<(r%23)) & 0x7ACCA0L )          goto ERR;
  if ( (1L<<(r%29)) & 0xC2EDD0CL )         goto ERR;
  if ( (1L<<(r%31)) & 0x6DE2B848L )        goto ERR;

  /* Final check - is sqr(sqrt(arg)) == arg ? */
  if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
     goto ERR;
  }
  if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
     goto ERR;
  }

  *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
ERR:mp_clear(&t);
  return res;
}
Example #12
0
File: rsa.c Project: JamieYan/wine
int rsa_make_key(int size, long e, rsa_key *key)
{
    mp_int p, q, tmp1, tmp2, tmp3;
    int    err;

    if ((size < (MIN_RSA_SIZE/8)) || (size > (MAX_RSA_SIZE/8))) {
        return CRYPT_INVALID_KEYSIZE;
    }

    if ((e < 3) || ((e & 1) == 0)) {
        return CRYPT_INVALID_ARG;
    }

    if ((err = mp_init_multi(&p, &q, &tmp1, &tmp2, &tmp3, NULL)) != MP_OKAY) {
        return mpi_to_ltc_error(err);
    }

    /* make primes p and q (optimization provided by Wayne Scott) */
    if ((err = mp_set_int(&tmp3, e)) != MP_OKAY) {
        goto error;    /* tmp3 = e */
    }

    /* make prime "p" */
    do {
        if ((err = rand_prime(&p, size*4)) != CRYPT_OK) {
            goto done;
        }
        if ((err = mp_sub_d(&p, 1, &tmp1)) != MP_OKAY)               {
            goto error;    /* tmp1 = p-1 */
        }
        if ((err = mp_gcd(&tmp1, &tmp3, &tmp2)) != MP_OKAY)          {
            goto error;    /* tmp2 = gcd(p-1, e) */
        }
    } while (mp_cmp_d(&tmp2, 1) != 0);                                                /* while e divides p-1 */

    /* make prime "q" */
    do {
        if ((err = rand_prime(&q, size*4)) != CRYPT_OK) {
            goto done;
        }
        if ((err = mp_sub_d(&q, 1, &tmp1)) != MP_OKAY)               {
            goto error;    /* tmp1 = q-1 */
        }
        if ((err = mp_gcd(&tmp1, &tmp3, &tmp2)) != MP_OKAY)          {
            goto error;    /* tmp2 = gcd(q-1, e) */
        }
    } while (mp_cmp_d(&tmp2, 1) != 0);                                               /* while e divides q-1 */

    /* tmp1 = lcm(p-1, q-1) */
    if ((err = mp_sub_d(&p, 1, &tmp2)) != MP_OKAY)                  {
        goto error;    /* tmp2 = p-1 */
    }
    /* tmp1 = q-1 (previous do/while loop) */
    if ((err = mp_lcm(&tmp1, &tmp2, &tmp1)) != MP_OKAY)             {
        goto error;    /* tmp1 = lcm(p-1, q-1) */
    }

    /* make key */
    if ((err = mp_init_multi(&key->e, &key->d, &key->N, &key->dQ, &key->dP,
                             &key->qP, &key->p, &key->q, NULL)) != MP_OKAY) {
        goto error;
    }

    if ((err = mp_set_int(&key->e, e)) != MP_OKAY)                     {
        goto error2;    /* key->e =  e */
    }
    if ((err = mp_invmod(&key->e, &tmp1, &key->d)) != MP_OKAY)         {
        goto error2;    /* key->d = 1/e mod lcm(p-1,q-1) */
    }
    if ((err = mp_mul(&p, &q, &key->N)) != MP_OKAY)                    {
        goto error2;    /* key->N = pq */
    }

    /* optimize for CRT now */
    /* find d mod q-1 and d mod p-1 */
    if ((err = mp_sub_d(&p, 1, &tmp1)) != MP_OKAY)                     {
        goto error2;    /* tmp1 = q-1 */
    }
    if ((err = mp_sub_d(&q, 1, &tmp2)) != MP_OKAY)                     {
        goto error2;    /* tmp2 = p-1 */
    }
    if ((err = mp_mod(&key->d, &tmp1, &key->dP)) != MP_OKAY)           {
        goto error2;    /* dP = d mod p-1 */
    }
    if ((err = mp_mod(&key->d, &tmp2, &key->dQ)) != MP_OKAY)           {
        goto error2;    /* dQ = d mod q-1 */
    }
    if ((err = mp_invmod(&q, &p, &key->qP)) != MP_OKAY)                {
        goto error2;    /* qP = 1/q mod p */
    }

    if ((err = mp_copy(&p, &key->p)) != MP_OKAY)                       {
        goto error2;
    }
    if ((err = mp_copy(&q, &key->q)) != MP_OKAY)                       {
        goto error2;
    }

    /* shrink ram required  */
    if ((err = mp_shrink(&key->e)) != MP_OKAY)                         {
        goto error2;
    }
    if ((err = mp_shrink(&key->d)) != MP_OKAY)                         {
        goto error2;
    }
    if ((err = mp_shrink(&key->N)) != MP_OKAY)                         {
        goto error2;
    }
    if ((err = mp_shrink(&key->dQ)) != MP_OKAY)                        {
        goto error2;
    }
    if ((err = mp_shrink(&key->dP)) != MP_OKAY)                        {
        goto error2;
    }
    if ((err = mp_shrink(&key->qP)) != MP_OKAY)                        {
        goto error2;
    }
    if ((err = mp_shrink(&key->p)) != MP_OKAY)                         {
        goto error2;
    }
    if ((err = mp_shrink(&key->q)) != MP_OKAY)                         {
        goto error2;
    }

    /* set key type (in this case it's CRT optimized) */
    key->type = PK_PRIVATE;

    /* return ok and free temps */
    err       = CRYPT_OK;
    goto done;
error2:
    mp_clear_multi(&key->d, &key->e, &key->N, &key->dQ, &key->dP,
                   &key->qP, &key->p, &key->q, NULL);
error:
    err = mpi_to_ltc_error(err);
done:
    mp_clear_multi(&tmp3, &tmp2, &tmp1, &p, &q, NULL);
    return err;
}
Example #13
0
int pb_sub(pb_poly *a, pb_poly *b, pb_poly *c)
{
   int neg, err, x, y, z, characteristic;
   pb_poly *tmp;

   /* grow c to be the max size */
   y = MAX(a->used, b->used);
   if (c->alloc < y) {
      if ((err = pb_grow(c, y)) != MP_OKAY) {
         return err;
      }
   }
   
   /* do we need to concern char */
   characteristic = mp_iszero(&(c->characteristic));

   /* sub the terms */
   z = MIN(a->used, b->used);
   for (x = 0; x < z; x++) {
       if ((err = mp_sub(&(a->terms[x]), &(b->terms[x]), &(c->terms[x]))) != MP_OKAY) {
          return err;
       }
       if (characteristic == MP_NO) {
          if ((err = mp_mod(&(c->terms[x]), &(c->characteristic), &(c->terms[x]))) != MP_OKAY) {
             return err;
          }
       }
   }

   /* excess digits? */
   if (y != z) {
       if (a->used == y) {
          tmp = a;
          neg = 0;
       } else {
          tmp = b;
          neg = 1;
       }
       for (x = z; x < y; x++) {
          if (characteristic == MP_NO) {
             if ((err = mp_mod(&(tmp->terms[x]), &(c->characteristic), &(c->terms[x]))) != MP_OKAY) {
                return err;
             }
             if (neg) {
                if ((err = mp_sub(&(c->characteristic), &(c->terms[x]), &(c->terms[x]))) != MP_OKAY) {
                   return err;
                }
             }
          } else {
             if (neg) {
                if ((err = mp_neg(&(tmp->terms[x]), &(c->terms[x]))) != MP_OKAY) {
                   return err; 
                }
             } else {
                if ((err = mp_copy(&(tmp->terms[x]), &(c->terms[x]))) != MP_OKAY) {
                   return err;
                }
             }
          }
       }
   }
   
   /* zero excess */
   for (x = y; x < c->used; x++) {
       mp_zero(&(c->terms[x]));
   }
   c->used = y;
   pb_clamp(c);

   return MP_OKAY;
}
/* hac 14.61, pp608 */
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, A, B, C, D;
  int     res;

  /* b cannot be negative */
  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
    return MP_VAL;
  }

  /* init temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, 
                           &A, &B, &C, &D, NULL)) != MP_OKAY) {
     return res;
  }

  /* x = a, y = b */
  if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
      goto LBL_ERR;
  }
  if ((res = mp_copy (b, &y)) != MP_OKAY) {
    goto LBL_ERR;
  }

  /* 2. [modified] if x,y are both even then return an error! */
  if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
    res = MP_VAL;
    goto LBL_ERR;
  }

  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
    goto LBL_ERR;
  }
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
    goto LBL_ERR;
  }
  mp_set (&A, 1);
  mp_set (&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven (&u) == 1) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if A or B is odd then */
    if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
      /* A = (A+y)/2, B = (B-x)/2 */
      if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
         goto LBL_ERR;
      }
    }
    /* A = A/2, B = B/2 */
    if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
      goto LBL_ERR;
    }
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven (&v) == 1) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if C or D is odd then */
    if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
      /* C = (C+y)/2, D = (D-x)/2 */
      if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
         goto LBL_ERR;
      }
    }
    /* C = C/2, D = D/2 */
    if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
      goto LBL_ERR;
    }
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 6.  if u >= v then */
  if (mp_cmp (&u, &v) != MP_LT) {
    /* u = u - v, A = A - C, B = B - D */
    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  } else {
    /* v - v - u, C = C - A, D = D - B */
    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero (&u) == 0)
    goto top;

  /* now a = C, b = D, gcd == g*v */

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
    res = MP_VAL;
    goto LBL_ERR;
  }

  /* if its too low */
  while (mp_cmp_d(&C, 0) == MP_LT) {
      if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
  }
  
  /* too big */
  while (mp_cmp_mag(&C, b) != MP_LT) {
      if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
  }
  
  /* C is now the inverse */
  mp_exch (&C, c);
  res = MP_OKAY;
LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
  return res;
}
Example #15
0
/* Computes the ECDSA signature (a concatenation of two values r and s)
 * on the digest using the given key and the random value kb (used in
 * computing s).
 */
SECStatus 
ECDSA_SignDigestWithSeed(ECPrivateKey *key, SECItem *signature, 
    const SECItem *digest, const unsigned char *kb, const int kblen)
{
    SECStatus rv = SECFailure;
#ifdef NSS_ENABLE_ECC
    mp_int x1;
    mp_int d, k;     /* private key, random integer */
    mp_int r, s;     /* tuple (r, s) is the signature */
    mp_int n;
    mp_err err = MP_OKAY;
    ECParams *ecParams = NULL;
    SECItem kGpoint = { siBuffer, NULL, 0};
    int flen = 0;    /* length in bytes of the field size */
    unsigned olen;   /* length in bytes of the base point order */
    unsigned obits;  /* length in bits  of the base point order */

#if EC_DEBUG
    char mpstr[256];
#endif

    /* Initialize MPI integers. */
    /* must happen before the first potential call to cleanup */
    MP_DIGITS(&x1) = 0;
    MP_DIGITS(&d) = 0;
    MP_DIGITS(&k) = 0;
    MP_DIGITS(&r) = 0;
    MP_DIGITS(&s) = 0;
    MP_DIGITS(&n) = 0;

    /* Check args */
    if (!key || !signature || !digest || !kb || (kblen < 0)) {
	PORT_SetError(SEC_ERROR_INVALID_ARGS);
	goto cleanup;
    }

    ecParams = &(key->ecParams);
    flen = (ecParams->fieldID.size + 7) >> 3;
    olen = ecParams->order.len;  
    if (signature->data == NULL) {
	/* a call to get the signature length only */
	goto finish;
    }
    if (signature->len < 2*olen) {
	PORT_SetError(SEC_ERROR_OUTPUT_LEN);
	goto cleanup;
    }


    CHECK_MPI_OK( mp_init(&x1) );
    CHECK_MPI_OK( mp_init(&d) );
    CHECK_MPI_OK( mp_init(&k) );
    CHECK_MPI_OK( mp_init(&r) );
    CHECK_MPI_OK( mp_init(&s) );
    CHECK_MPI_OK( mp_init(&n) );

    SECITEM_TO_MPINT( ecParams->order, &n );
    SECITEM_TO_MPINT( key->privateValue, &d );

    CHECK_MPI_OK( mp_read_unsigned_octets(&k, kb, kblen) );
    /* Make sure k is in the interval [1, n-1] */
    if ((mp_cmp_z(&k) <= 0) || (mp_cmp(&k, &n) >= 0)) {
#if EC_DEBUG
        printf("k is outside [1, n-1]\n");
        mp_tohex(&k, mpstr);
	printf("k : %s \n", mpstr);
        mp_tohex(&n, mpstr);
	printf("n : %s \n", mpstr);
#endif
	PORT_SetError(SEC_ERROR_NEED_RANDOM);
	goto cleanup;
    }

    /*
    ** We do not want timing information to leak the length of k,
    ** so we compute k*G using an equivalent scalar of fixed
    ** bit-length.
    ** Fix based on patch for ECDSA timing attack in the paper
    ** by Billy Bob Brumley and Nicola Tuveri at
    **   http://eprint.iacr.org/2011/232
    **
    ** How do we convert k to a value of a fixed bit-length?
    ** k starts off as an integer satisfying 0 <= k < n.  Hence,
    ** n <= k+n < 2n, which means k+n has either the same number
    ** of bits as n or one more bit than n.  If k+n has the same
    ** number of bits as n, the second addition ensures that the
    ** final value has exactly one more bit than n.  Thus, we
    ** always end up with a value that exactly one more bit than n.
    */
    CHECK_MPI_OK( mp_add(&k, &n, &k) );
    if (mpl_significant_bits(&k) <= mpl_significant_bits(&n)) {
	CHECK_MPI_OK( mp_add(&k, &n, &k) );
    }

    /* 
    ** ANSI X9.62, Section 5.3.2, Step 2
    **
    ** Compute kG
    */
    kGpoint.len = 2*flen + 1;
    kGpoint.data = PORT_Alloc(2*flen + 1);
    if ((kGpoint.data == NULL) ||
	(ec_points_mul(ecParams, &k, NULL, NULL, &kGpoint)
	    != SECSuccess))
	goto cleanup;

    /* 
    ** ANSI X9.62, Section 5.3.3, Step 1
    **
    ** Extract the x co-ordinate of kG into x1
    */
    CHECK_MPI_OK( mp_read_unsigned_octets(&x1, kGpoint.data + 1, 
	                                  (mp_size) flen) );

    /* 
    ** ANSI X9.62, Section 5.3.3, Step 2
    **
    ** r = x1 mod n  NOTE: n is the order of the curve
    */
    CHECK_MPI_OK( mp_mod(&x1, &n, &r) );

    /*
    ** ANSI X9.62, Section 5.3.3, Step 3
    **
    ** verify r != 0 
    */
    if (mp_cmp_z(&r) == 0) {
	PORT_SetError(SEC_ERROR_NEED_RANDOM);
	goto cleanup;
    }

    /*                                  
    ** ANSI X9.62, Section 5.3.3, Step 4
    **
    ** s = (k**-1 * (HASH(M) + d*r)) mod n 
    */
    SECITEM_TO_MPINT(*digest, &s);        /* s = HASH(M)     */

    /* In the definition of EC signing, digests are truncated
     * to the length of n in bits. 
     * (see SEC 1 "Elliptic Curve Digit Signature Algorithm" section 4.1.*/
    CHECK_MPI_OK( (obits = mpl_significant_bits(&n)) );
    if (digest->len*8 > obits) {
	mpl_rsh(&s,&s,digest->len*8 - obits);
    }

#if EC_DEBUG
    mp_todecimal(&n, mpstr);
    printf("n : %s (dec)\n", mpstr);
    mp_todecimal(&d, mpstr);
    printf("d : %s (dec)\n", mpstr);
    mp_tohex(&x1, mpstr);
    printf("x1: %s\n", mpstr);
    mp_todecimal(&s, mpstr);
    printf("digest: %s (decimal)\n", mpstr);
    mp_todecimal(&r, mpstr);
    printf("r : %s (dec)\n", mpstr);
    mp_tohex(&r, mpstr);
    printf("r : %s\n", mpstr);
#endif

    CHECK_MPI_OK( mp_invmod(&k, &n, &k) );      /* k = k**-1 mod n */
    CHECK_MPI_OK( mp_mulmod(&d, &r, &n, &d) );  /* d = d * r mod n */
    CHECK_MPI_OK( mp_addmod(&s, &d, &n, &s) );  /* s = s + d mod n */
    CHECK_MPI_OK( mp_mulmod(&s, &k, &n, &s) );  /* s = s * k mod n */

#if EC_DEBUG
    mp_todecimal(&s, mpstr);
    printf("s : %s (dec)\n", mpstr);
    mp_tohex(&s, mpstr);
    printf("s : %s\n", mpstr);
#endif

    /*
    ** ANSI X9.62, Section 5.3.3, Step 5
    **
    ** verify s != 0
    */
    if (mp_cmp_z(&s) == 0) {
	PORT_SetError(SEC_ERROR_NEED_RANDOM);
	goto cleanup;
    }

   /*
    **
    ** Signature is tuple (r, s)
    */
    CHECK_MPI_OK( mp_to_fixlen_octets(&r, signature->data, olen) );
    CHECK_MPI_OK( mp_to_fixlen_octets(&s, signature->data + olen, olen) );
finish:
    signature->len = 2*olen;

    rv = SECSuccess;
    err = MP_OKAY;
cleanup:
    mp_clear(&x1);
    mp_clear(&d);
    mp_clear(&k);
    mp_clear(&r);
    mp_clear(&s);
    mp_clear(&n);

    if (kGpoint.data) {
	PORT_ZFree(kGpoint.data, 2*flen + 1);
    }

    if (err) {
	MP_TO_SEC_ERROR(err);
	rv = SECFailure;
    }

#if EC_DEBUG
    printf("ECDSA signing with seed %s\n",
	(rv == SECSuccess) ? "succeeded" : "failed");
#endif
#else
    PORT_SetError(SEC_ERROR_UNSUPPORTED_KEYALG);
#endif /* NSS_ENABLE_ECC */

   return rv;
}
Example #16
0
static int
ltm_rsa_generate_key(RSA *rsa, int bits, BIGNUM *e, BN_GENCB *cb)
{
    mp_int el, p, q, n, d, dmp1, dmq1, iqmp, t1, t2, t3;
    int counter, ret, bitsp;

    if (bits < 789)
	return -1;

    bitsp = (bits + 1) / 2;

    ret = -1;

    mp_init_multi(&el, &p, &q, &n, &d,
		  &dmp1, &dmq1, &iqmp,
		  &t1, &t2, &t3, NULL);

    BN2mpz(&el, e);

    /* generate p and q so that p != q and bits(pq) ~ bits */
    counter = 0;
    do {
	BN_GENCB_call(cb, 2, counter++);
	CHECK(random_num(&p, bitsp), 0);
	CHECK(mp_find_prime(&p,128), MP_YES);

	mp_sub_d(&p, 1, &t1);
	mp_gcd(&t1, &el, &t2);
    } while(mp_cmp_d(&t2, 1) != 0);

    BN_GENCB_call(cb, 3, 0);

    counter = 0;
    do {
	BN_GENCB_call(cb, 2, counter++);
	CHECK(random_num(&q, bits - bitsp), 0);
	CHECK(mp_find_prime(&q,128), MP_YES);

	if (mp_cmp(&p, &q) == 0) /* don't let p and q be the same */
	    continue;

	mp_sub_d(&q, 1, &t1);
	mp_gcd(&t1, &el, &t2);
    } while(mp_cmp_d(&t2, 1) != 0);

    /* make p > q */
    if (mp_cmp(&p, &q) < 0) {
	mp_int c;
	c = p;
	p = q;
	q = c;
    }

    BN_GENCB_call(cb, 3, 1);

    /* calculate n,  		n = p * q */
    mp_mul(&p, &q, &n);

    /* calculate d, 		d = 1/e mod (p - 1)(q - 1) */
    mp_sub_d(&p, 1, &t1);
    mp_sub_d(&q, 1, &t2);
    mp_mul(&t1, &t2, &t3);
    mp_invmod(&el, &t3, &d);

    /* calculate dmp1		dmp1 = d mod (p-1) */
    mp_mod(&d, &t1, &dmp1);
    /* calculate dmq1		dmq1 = d mod (q-1) */
    mp_mod(&d, &t2, &dmq1);
    /* calculate iqmp 		iqmp = 1/q mod p */
    mp_invmod(&q, &p, &iqmp);

    /* fill in RSA key */

    rsa->e = mpz2BN(&el);
    rsa->p = mpz2BN(&p);
    rsa->q = mpz2BN(&q);
    rsa->n = mpz2BN(&n);
    rsa->d = mpz2BN(&d);
    rsa->dmp1 = mpz2BN(&dmp1);
    rsa->dmq1 = mpz2BN(&dmq1);
    rsa->iqmp = mpz2BN(&iqmp);

    ret = 1;

out:
    mp_clear_multi(&el, &p, &q, &n, &d,
		   &dmp1, &dmq1, &iqmp,
		   &t1, &t2, &t3, NULL);

    return ret;
}
Example #17
0
/*
** Checks the signature on the given digest using the key provided.
*/
SECStatus 
ECDSA_VerifyDigest(ECPublicKey *key, const SECItem *signature, 
                 const SECItem *digest)
{
    SECStatus rv = SECFailure;
#ifdef NSS_ENABLE_ECC
    mp_int r_, s_;           /* tuple (r', s') is received signature) */
    mp_int c, u1, u2, v;     /* intermediate values used in verification */
    mp_int x1;
    mp_int n;
    mp_err err = MP_OKAY;
    ECParams *ecParams = NULL;
    SECItem pointC = { siBuffer, NULL, 0 };
    int slen;       /* length in bytes of a half signature (r or s) */
    int flen;       /* length in bytes of the field size */
    unsigned olen;  /* length in bytes of the base point order */
    unsigned obits; /* length in bits  of the base point order */

#if EC_DEBUG
    char mpstr[256];
    printf("ECDSA verification called\n");
#endif

    /* Initialize MPI integers. */
    /* must happen before the first potential call to cleanup */
    MP_DIGITS(&r_) = 0;
    MP_DIGITS(&s_) = 0;
    MP_DIGITS(&c) = 0;
    MP_DIGITS(&u1) = 0;
    MP_DIGITS(&u2) = 0;
    MP_DIGITS(&x1) = 0;
    MP_DIGITS(&v)  = 0;
    MP_DIGITS(&n)  = 0;

    /* Check args */
    if (!key || !signature || !digest) {
	PORT_SetError(SEC_ERROR_INVALID_ARGS);
	goto cleanup;
    }

    ecParams = &(key->ecParams);
    flen = (ecParams->fieldID.size + 7) >> 3;  
    olen = ecParams->order.len;  
    if (signature->len == 0 || signature->len%2 != 0 ||
	signature->len > 2*olen) {
	PORT_SetError(SEC_ERROR_INPUT_LEN);
	goto cleanup;
    }
    slen = signature->len/2;

    SECITEM_AllocItem(NULL, &pointC, 2*flen + 1);
    if (pointC.data == NULL)
	goto cleanup;

    CHECK_MPI_OK( mp_init(&r_) );
    CHECK_MPI_OK( mp_init(&s_) );
    CHECK_MPI_OK( mp_init(&c)  );
    CHECK_MPI_OK( mp_init(&u1) );
    CHECK_MPI_OK( mp_init(&u2) );
    CHECK_MPI_OK( mp_init(&x1)  );
    CHECK_MPI_OK( mp_init(&v)  );
    CHECK_MPI_OK( mp_init(&n)  );

    /*
    ** Convert received signature (r', s') into MPI integers.
    */
    CHECK_MPI_OK( mp_read_unsigned_octets(&r_, signature->data, slen) );
    CHECK_MPI_OK( mp_read_unsigned_octets(&s_, signature->data + slen, slen) );
                                          
    /* 
    ** ANSI X9.62, Section 5.4.2, Steps 1 and 2
    **
    ** Verify that 0 < r' < n and 0 < s' < n
    */
    SECITEM_TO_MPINT(ecParams->order, &n);
    if (mp_cmp_z(&r_) <= 0 || mp_cmp_z(&s_) <= 0 ||
        mp_cmp(&r_, &n) >= 0 || mp_cmp(&s_, &n) >= 0) {
	PORT_SetError(SEC_ERROR_BAD_SIGNATURE);
	goto cleanup; /* will return rv == SECFailure */
    }

    /*
    ** ANSI X9.62, Section 5.4.2, Step 3
    **
    ** c = (s')**-1 mod n
    */
    CHECK_MPI_OK( mp_invmod(&s_, &n, &c) );      /* c = (s')**-1 mod n */

    /*
    ** ANSI X9.62, Section 5.4.2, Step 4
    **
    ** u1 = ((HASH(M')) * c) mod n
    */
    SECITEM_TO_MPINT(*digest, &u1);                  /* u1 = HASH(M)     */

    /* In the definition of EC signing, digests are truncated
     * to the length of n in bits. 
     * (see SEC 1 "Elliptic Curve Digit Signature Algorithm" section 4.1.*/
    CHECK_MPI_OK( (obits = mpl_significant_bits(&n)) );
    if (digest->len*8 > obits) {  /* u1 = HASH(M')     */
	mpl_rsh(&u1,&u1,digest->len*8 - obits);
    }

#if EC_DEBUG
    mp_todecimal(&r_, mpstr);
    printf("r_: %s (dec)\n", mpstr);
    mp_todecimal(&s_, mpstr);
    printf("s_: %s (dec)\n", mpstr);
    mp_todecimal(&c, mpstr);
    printf("c : %s (dec)\n", mpstr);
    mp_todecimal(&u1, mpstr);
    printf("digest: %s (dec)\n", mpstr);
#endif

    CHECK_MPI_OK( mp_mulmod(&u1, &c, &n, &u1) );  /* u1 = u1 * c mod n */

    /*
    ** ANSI X9.62, Section 5.4.2, Step 4
    **
    ** u2 = ((r') * c) mod n
    */
    CHECK_MPI_OK( mp_mulmod(&r_, &c, &n, &u2) );

    /*
    ** ANSI X9.62, Section 5.4.3, Step 1
    **
    ** Compute u1*G + u2*Q
    ** Here, A = u1.G     B = u2.Q    and   C = A + B
    ** If the result, C, is the point at infinity, reject the signature
    */
    if (ec_points_mul(ecParams, &u1, &u2, &key->publicValue, &pointC)
	!= SECSuccess) {
	rv = SECFailure;
	goto cleanup;
    }
    if (ec_point_at_infinity(&pointC)) {
	PORT_SetError(SEC_ERROR_BAD_SIGNATURE);
	rv = SECFailure;
	goto cleanup;
    }

    CHECK_MPI_OK( mp_read_unsigned_octets(&x1, pointC.data + 1, flen) );

    /*
    ** ANSI X9.62, Section 5.4.4, Step 2
    **
    ** v = x1 mod n
    */
    CHECK_MPI_OK( mp_mod(&x1, &n, &v) );

#if EC_DEBUG
    mp_todecimal(&r_, mpstr);
    printf("r_: %s (dec)\n", mpstr);
    mp_todecimal(&v, mpstr);
    printf("v : %s (dec)\n", mpstr);
#endif

    /*
    ** ANSI X9.62, Section 5.4.4, Step 3
    **
    ** Verification:  v == r'
    */
    if (mp_cmp(&v, &r_)) {
	PORT_SetError(SEC_ERROR_BAD_SIGNATURE);
	rv = SECFailure; /* Signature failed to verify. */
    } else {
	rv = SECSuccess; /* Signature verified. */
    }

#if EC_DEBUG
    mp_todecimal(&u1, mpstr);
    printf("u1: %s (dec)\n", mpstr);
    mp_todecimal(&u2, mpstr);
    printf("u2: %s (dec)\n", mpstr);
    mp_tohex(&x1, mpstr);
    printf("x1: %s\n", mpstr);
    mp_todecimal(&v, mpstr);
    printf("v : %s (dec)\n", mpstr);
#endif

cleanup:
    mp_clear(&r_);
    mp_clear(&s_);
    mp_clear(&c);
    mp_clear(&u1);
    mp_clear(&u2);
    mp_clear(&x1);
    mp_clear(&v);
    mp_clear(&n);

    if (pointC.data) SECITEM_FreeItem(&pointC, PR_FALSE);
    if (err) {
	MP_TO_SEC_ERROR(err);
	rv = SECFailure;
    }

#if EC_DEBUG
    printf("ECDSA verification %s\n",
	(rv == SECSuccess) ? "succeeded" : "failed");
#endif
#else
    PORT_SetError(SEC_ERROR_UNSUPPORTED_KEYALG);
#endif /* NSS_ENABLE_ECC */

    return rv;
}
Example #18
0
/**
  Sign a hash with DSA
  @param in       The hash to sign
  @param inlen    The length of the hash to sign
  @param r        The "r" integer of the signature (caller must initialize with mp_init() first)
  @param s        The "s" integer of the signature (caller must initialize with mp_init() first)
  @param key      A private DSA key
  @return CRYPT_OK if successful
*/
int dsa_sign_hash_raw(const unsigned char *in, unsigned long inlen,
		      mp_int_t r, mp_int_t s, dsa_key * key)
{
	mp_int k, kinv, tmp;
	unsigned char *buf;
	int err;

	LTC_ARGCHK(in != NULL);
	LTC_ARGCHK(r != NULL);
	LTC_ARGCHK(s != NULL);
	LTC_ARGCHK(key != NULL);

	if (key->type != PK_PRIVATE) {
		return CRYPT_PK_NOT_PRIVATE;
	}

	/* check group order size  */
	if (key->qord >= LTC_MDSA_MAX_GROUP) {
		return CRYPT_INVALID_ARG;
	}

	buf = XMALLOC(LTC_MDSA_MAX_GROUP);
	if (buf == NULL) {
		return CRYPT_MEM;
	}

	/* Init our temps */
	if ((err = mp_init_multi(&k, &kinv, &tmp, NULL)) != CRYPT_OK) {
		goto ERRBUF;
	}

retry:

	do {
		/* gen random k */
		get_random_bytes(buf, key->qord);

		/* read k */
		if ((err =
		     mp_read_unsigned_bin(&k, buf, key->qord)) != CRYPT_OK) {
			goto error;
		}

		/* k > 1 ? */
		if (mp_cmp_d(&k, 1) != LTC_MP_GT) {
			goto retry;
		}

		/* test gcd */
		if ((err = mp_gcd(&k, &key->q, &tmp)) != CRYPT_OK) {
			goto error;
		}
	} while (mp_cmp_d(&tmp, 1) != LTC_MP_EQ);

	/* now find 1/k mod q */
	if ((err = mp_invmod(&k, &key->q, &kinv)) != CRYPT_OK) {
		goto error;
	}

	/* now find r = g^k mod p mod q */
	if ((err = mp_exptmod(&key->g, &k, &key->p, r)) != CRYPT_OK) {
		goto error;
	}
	if ((err = mp_mod(r, &key->q, r)) != CRYPT_OK) {
		goto error;
	}

	if (mp_iszero(r) == LTC_MP_YES) {
		goto retry;
	}

	/* now find s = (in + xr)/k mod q */
	if ((err =
	     mp_read_unsigned_bin(&tmp, (unsigned char *)in,
				  inlen)) != CRYPT_OK) {
		goto error;
	}
	if ((err = mp_mul(&key->x, r, s)) != CRYPT_OK) {
		goto error;
	}
	if ((err = mp_add(s, &tmp, s)) != CRYPT_OK) {
		goto error;
	}
	if ((err = mp_mulmod(s, &kinv, &key->q, s)) != CRYPT_OK) {
		goto error;
	}

	if (mp_iszero(s) == LTC_MP_YES) {
		goto retry;
	}

	err = CRYPT_OK;
error:
	mp_clear_multi(&k, &kinv, &tmp, NULL);
ERRBUF:
#ifdef LTC_CLEAN_STACK
	zeromem(buf, LTC_MDSA_MAX_GROUP);
#endif
	XFREE(buf);
	return err;
}
/*
    Strong Lucas-Selfridge test.
    returns MP_YES if it is a strong L-S prime, MP_NO if it is composite

    Code ported from  Thomas Ray Nicely's implementation of the BPSW test
    at http://www.trnicely.net/misc/bpsw.html

    Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>.
    Released into the public domain by the author, who disclaims any legal
    liability arising from its use

    The multi-line comments are made by Thomas R. Nicely and are copied verbatim.
    Additional comments marked "CZ" (without the quotes) are by the code-portist.

    (If that name sounds familiar, he is the guy who found the fdiv bug in the
     Pentium (P5x, I think) Intel processor)
*/
int mp_prime_strong_lucas_selfridge(const mp_int *a, int *result)
{
   /* CZ TODO: choose better variable names! */
   mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz;
   /* CZ TODO: Some of them need the full 32 bit, hence the (temporary) exclusion of MP_8BIT */
   int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits;
   int e;
   int isset;

   *result = MP_NO;

   /*
   Find the first element D in the sequence {5, -7, 9, -11, 13, ...}
   such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory
   indicates that, if N is not a perfect square, D will "nearly
   always" be "small." Just in case, an overflow trap for D is
   included.
   */

   if ((e = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz,
                          NULL)) != MP_OKAY) {
      return e;
   }

   D = 5;
   sign = 1;

   for (;;) {
      Ds   = sign * D;
      sign = -sign;
      if ((e = mp_set_long(&Dz, (unsigned long)D)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      /* if 1 < GCD < N then N is composite with factor "D", and
         Jacobi(D,N) is technically undefined (but often returned
         as zero). */
      if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) {
         goto LBL_LS_ERR;
      }
      if (Ds < 0) {
         Dz.sign = MP_NEG;
      }
      if ((e = mp_kronecker(&Dz, a, &J)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }

      if (J == -1) {
         break;
      }
      D += 2;

      if (D > (INT_MAX - 2)) {
         e = MP_VAL;
         goto LBL_LS_ERR;
      }
   }

   P = 1;              /* Selfridge's choice */
   Q = (1 - Ds) / 4;   /* Required so D = P*P - 4*Q */

   /* NOTE: The conditions (a) N does not divide Q, and
      (b) D is square-free or not a perfect square, are included by
      some authors; e.g., "Prime numbers and computer methods for
      factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston),
      p. 130. For this particular application of Lucas sequences,
      these conditions were found to be immaterial. */

   /* Now calculate N - Jacobi(D,N) = N + 1 (even), and calculate the
      odd positive integer d and positive integer s for which
      N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test).
      The strong Lucas-Selfridge test then returns N as a strong
      Lucas probable prime (slprp) if any of the following
      conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0,
      V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0
      (all equalities mod N). Thus d is the highest index of U that
      must be computed (since V_2m is independent of U), compared
      to U_{N+1} for the standard Lucas-Selfridge test; and no
      index of V beyond (N+1)/2 is required, just as in the
      standard Lucas-Selfridge test. However, the quantity Q^d must
      be computed for use (if necessary) in the latter stages of
      the test. The result is that the strong Lucas-Selfridge test
      has a running time only slightly greater (order of 10 %) than
      that of the standard Lucas-Selfridge test, while producing
      only (roughly) 30 % as many pseudoprimes (and every strong
      Lucas pseudoprime is also a standard Lucas pseudoprime). Thus
      the evidence indicates that the strong Lucas-Selfridge test is
      more effective than the standard Lucas-Selfridge test, and a
      Baillie-PSW test based on the strong Lucas-Selfridge test
      should be more reliable. */

   if ((e = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) {
      goto LBL_LS_ERR;
   }
   s = mp_cnt_lsb(&Np1);

   /* CZ
    * This should round towards zero because
    * Thomas R. Nicely used GMP's mpz_tdiv_q_2exp()
    * and mp_div_2d() is equivalent. Additionally:
    * dividing an even number by two does not produce
    * any leftovers.
    */
   if ((e = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) {
      goto LBL_LS_ERR;
   }
   /* We must now compute U_d and V_d. Since d is odd, the accumulated
      values U and V are initialized to U_1 and V_1 (if the target
      index were even, U and V would be initialized instead to U_0=0
      and V_0=2). The values of U_2m and V_2m are also initialized to
      U_1 and V_1; the FOR loop calculates in succession U_2 and V_2,
      U_4 and V_4, U_8 and V_8, etc. If the corresponding bits
      (1, 2, 3, ...) of t are on (the zero bit having been accounted
      for in the initialization of U and V), these values are then
      combined with the previous totals for U and V, using the
      composition formulas for addition of indices. */

   mp_set(&Uz, 1uL);    /* U=U_1 */
   mp_set(&Vz, (mp_digit)P);    /* V=V_1 */
   mp_set(&U2mz, 1uL);  /* U_1 */
   mp_set(&V2mz, (mp_digit)P);  /* V_1 */

   if (Q < 0) {
      Q = -Q;
      if ((e = mp_set_long(&Qmz, (unsigned long)Q)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      /* Initializes calculation of Q^d */
      if ((e = mp_set_long(&Qkdz, (unsigned long)Q)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      Qmz.sign = MP_NEG;
      Q2mz.sign = MP_NEG;
      Qkdz.sign = MP_NEG;
      Q = -Q;
   } else {
      if ((e = mp_set_long(&Qmz, (unsigned long)Q)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      /* Initializes calculation of Q^d */
      if ((e = mp_set_long(&Qkdz, (unsigned long)Q)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
   }

   Nbits = mp_count_bits(&Dz);
   for (u = 1; u < Nbits; u++) { /* zero bit off, already accounted for */
      /* Formulas for doubling of indices (carried out mod N). Note that
       * the indices denoted as "2m" are actually powers of 2, specifically
       * 2^(ul-1) beginning each loop and 2^ul ending each loop.
       *
       * U_2m = U_m*V_m
       * V_2m = V_m*V_m - 2*Q^m
       */

      if ((e = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      /* Must calculate powers of Q for use in V_2m, also for Q^d later */
      if ((e = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      /* prevents overflow */ /* CZ  still necessary without a fixed prealloc'd mem.? */
      if ((e = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }

      if ((isset = mp_get_bit(&Dz, u)) == MP_VAL) {
         e = isset;
         goto LBL_LS_ERR;
      }
      if (isset == MP_YES) {
         /* Formulas for addition of indices (carried out mod N);
          *
          * U_(m+n) = (U_m*V_n + U_n*V_m)/2
          * V_(m+n) = (V_m*V_n + D*U_m*U_n)/2
          *
          * Be careful with division by 2 (mod N)!
          */

         if ((e = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = s_mp_mul_si(&T4z, (long)Ds, &T4z)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if (mp_isodd(&Uz) != MP_NO) {
            if ((e = mp_add(&Uz, a, &Uz)) != MP_OKAY) {
               goto LBL_LS_ERR;
            }
         }
         /* CZ
          * This should round towards negative infinity because
          * Thomas R. Nicely used GMP's mpz_fdiv_q_2exp().
          * But mp_div_2() does not do so, it is truncating instead.
          */
         if ((e = mp_div_2(&Uz, &Uz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((Uz.sign == MP_NEG) && (mp_isodd(&Uz) != MP_NO)) {
            if ((e = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) {
               goto LBL_LS_ERR;
            }
         }
         if ((e = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if (mp_isodd(&Vz) != MP_NO) {
            if ((e = mp_add(&Vz, a, &Vz)) != MP_OKAY) {
               goto LBL_LS_ERR;
            }
         }
         if ((e = mp_div_2(&Vz, &Vz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((Vz.sign == MP_NEG) && (mp_isodd(&Vz) != MP_NO)) {
            if ((e = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) {
               goto LBL_LS_ERR;
            }
         }
         if ((e = mp_mod(&Uz, a, &Uz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mod(&Vz, a, &Vz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         /* Calculating Q^d for later use */
         if ((e = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
      }
   }

   /* If U_d or V_d is congruent to 0 mod N, then N is a prime or a
      strong Lucas pseudoprime. */
   if ((mp_iszero(&Uz) != MP_NO) || (mp_iszero(&Vz) != MP_NO)) {
      *result = MP_YES;
      goto LBL_LS_ERR;
   }

   /* NOTE: Ribenboim ("The new book of prime number records," 3rd ed.,
      1995/6) omits the condition V0 on p.142, but includes it on
      p. 130. The condition is NECESSARY; otherwise the test will
      return false negatives---e.g., the primes 29 and 2000029 will be
      returned as composite. */

   /* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d}
      by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of
      these are congruent to 0 mod N, then N is a prime or a strong
      Lucas pseudoprime. */

   /* Initialize 2*Q^(d*2^r) for V_2m */
   if ((e = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) {
      goto LBL_LS_ERR;
   }

   for (r = 1; r < s; r++) {
      if ((e = mp_sqr(&Vz, &Vz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mod(&Vz, a, &Vz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if (mp_iszero(&Vz) != MP_NO) {
         *result = MP_YES;
         goto LBL_LS_ERR;
      }
      /* Calculate Q^{d*2^r} for next r (final iteration irrelevant). */
      if (r < (s - 1)) {
         if ((e = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
      }
   }
LBL_LS_ERR:
   mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL);
   return e;
}
Example #20
0
/**
   Verify an ECC signature
   @param sig         The signature to verify
   @param siglen      The length of the signature (octets)
   @param hash        The hash (message digest) that was signed
   @param hashlen     The length of the hash (octets)
   @param stat        Result of signature, 1==valid, 0==invalid
   @param key         The corresponding public ECC key
   @return CRYPT_OK if successful (even if the signature is not valid)
*/
int ecc_verify_hash(const unsigned char *sig,  unsigned long siglen,
                    const unsigned char *hash, unsigned long hashlen, 
                    int *stat, ecc_key *key)
{
   ecc_point    *mG, *mQ;
   void          *r, *s, *v, *w, *u1, *u2, *e, *p, *m;
   void          *mp;
   int           err;

   LTC_ARGCHK(sig  != NULL);
   LTC_ARGCHK(hash != NULL);
   LTC_ARGCHK(stat != NULL);
   LTC_ARGCHK(key  != NULL);

   /* default to invalid signature */
   *stat = 0;
   mp    = NULL;

   /* is the IDX valid ?  */
   if (ltc_ecc_is_valid_idx(key->idx) != 1) {
      return CRYPT_PK_INVALID_TYPE;
   }

   /* allocate ints */
   if ((err = mp_init_multi(&r, &s, &v, &w, &u1, &u2, &p, &e, &m, NULL)) != CRYPT_OK) {
      return CRYPT_MEM;
   }

   /* allocate points */
   mG = ltc_ecc_new_point();
   mQ = ltc_ecc_new_point();
   if (mQ  == NULL || mG == NULL) {
      err = CRYPT_MEM;
      goto error;
   }

   /* parse header */
   if ((err = der_decode_sequence_multi(sig, siglen,
                                  LTC_ASN1_INTEGER, 1UL, r,
                                  LTC_ASN1_INTEGER, 1UL, s,
                                  LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) {
      goto error;
   }

   /* get the order */
   if ((err = mp_read_radix(p, (char *)key->dp->order, 16)) != CRYPT_OK)                                { goto error; }

   /* get the modulus */
   if ((err = mp_read_radix(m, (char *)key->dp->prime, 16)) != CRYPT_OK)                                { goto error; }

   /* check for zero */
   if (mp_iszero(r) || mp_iszero(s) || mp_cmp(r, p) != LTC_MP_LT || mp_cmp(s, p) != LTC_MP_LT) {
      err = CRYPT_INVALID_PACKET;
      goto error;
   }

   /* read hash */
   if ((err = mp_read_unsigned_bin(e, (unsigned char *)hash, (int)hashlen)) != CRYPT_OK)                { goto error; }

   /*  w  = s^-1 mod n */
   if ((err = mp_invmod(s, p, w)) != CRYPT_OK)                                                          { goto error; }

   /* u1 = ew */
   if ((err = mp_mulmod(e, w, p, u1)) != CRYPT_OK)                                                      { goto error; }

   /* u2 = rw */
   if ((err = mp_mulmod(r, w, p, u2)) != CRYPT_OK)                                                      { goto error; }

   /* find mG and mQ */
   if ((err = mp_read_radix(mG->x, (char *)key->dp->Gx, 16)) != CRYPT_OK)                               { goto error; }
   if ((err = mp_read_radix(mG->y, (char *)key->dp->Gy, 16)) != CRYPT_OK)                               { goto error; }
   if ((err = mp_set(mG->z, 1)) != CRYPT_OK)                                                            { goto error; }

   if ((err = mp_copy(key->pubkey.x, mQ->x)) != CRYPT_OK)                                               { goto error; }
   if ((err = mp_copy(key->pubkey.y, mQ->y)) != CRYPT_OK)                                               { goto error; }
   if ((err = mp_copy(key->pubkey.z, mQ->z)) != CRYPT_OK)                                               { goto error; }

   /* compute u1*mG + u2*mQ = mG */
   if (ltc_mp.ecc_mul2add == NULL) {
      if ((err = ltc_mp.ecc_ptmul(u1, mG, mG, m, 0)) != CRYPT_OK)                                       { goto error; }
      if ((err = ltc_mp.ecc_ptmul(u2, mQ, mQ, m, 0)) != CRYPT_OK)                                       { goto error; }
  
      /* find the montgomery mp */
      if ((err = mp_montgomery_setup(m, &mp)) != CRYPT_OK)                                              { goto error; }

      /* add them */
      if ((err = ltc_mp.ecc_ptadd(mQ, mG, mG, m, mp)) != CRYPT_OK)                                      { goto error; }
   
      /* reduce */
      if ((err = ltc_mp.ecc_map(mG, m, mp)) != CRYPT_OK)                                                { goto error; }
   } else {
      /* use Shamir's trick to compute u1*mG + u2*mQ using half of the doubles */
      if ((err = ltc_mp.ecc_mul2add(mG, u1, mQ, u2, mG, m)) != CRYPT_OK)                                { goto error; }
   }

   /* v = X_x1 mod n */
   if ((err = mp_mod(mG->x, p, v)) != CRYPT_OK)                                                         { goto error; }

   /* does v == r */
   if (mp_cmp(v, r) == LTC_MP_EQ) {
      *stat = 1;
   }

   /* clear up and return */
   err = CRYPT_OK;
error:
   ltc_ecc_del_point(mG);
   ltc_ecc_del_point(mQ);
   mp_clear_multi(r, s, v, w, u1, u2, p, e, m, NULL);
   if (mp != NULL) { 
      mp_montgomery_free(mp);
   }
   return err;
}
Example #21
0
static SECStatus
rsa_build_from_primes(mp_int *p, mp_int *q, 
		mp_int *e, PRBool needPublicExponent, 
		mp_int *d, PRBool needPrivateExponent,
		RSAPrivateKey *key, unsigned int keySizeInBits)
{
    mp_int n, phi;
    mp_int psub1, qsub1, tmp;
    mp_err   err = MP_OKAY;
    SECStatus rv = SECSuccess;
    MP_DIGITS(&n)     = 0;
    MP_DIGITS(&phi)   = 0;
    MP_DIGITS(&psub1) = 0;
    MP_DIGITS(&qsub1) = 0;
    MP_DIGITS(&tmp)   = 0;
    CHECK_MPI_OK( mp_init(&n)     );
    CHECK_MPI_OK( mp_init(&phi)   );
    CHECK_MPI_OK( mp_init(&psub1) );
    CHECK_MPI_OK( mp_init(&qsub1) );
    CHECK_MPI_OK( mp_init(&tmp)   );
    /* 1.  Compute n = p*q */
    CHECK_MPI_OK( mp_mul(p, q, &n) );
    /*     verify that the modulus has the desired number of bits */
    if ((unsigned)mpl_significant_bits(&n) != keySizeInBits) {
	PORT_SetError(SEC_ERROR_NEED_RANDOM);
	rv = SECFailure;
	goto cleanup;
    }

    /* at least one exponent must be given */
    PORT_Assert(!(needPublicExponent && needPrivateExponent));

    /* 2.  Compute phi = (p-1)*(q-1) */
    CHECK_MPI_OK( mp_sub_d(p, 1, &psub1) );
    CHECK_MPI_OK( mp_sub_d(q, 1, &qsub1) );
    if (needPublicExponent || needPrivateExponent) {
	CHECK_MPI_OK( mp_mul(&psub1, &qsub1, &phi) );
	/* 3.  Compute d = e**-1 mod(phi) */
	/*     or      e = d**-1 mod(phi) as necessary */
	if (needPublicExponent) {
	    err = mp_invmod(d, &phi, e);
	} else {
	    err = mp_invmod(e, &phi, d);
	}
    } else {
	err = MP_OKAY;
    }
    /*     Verify that phi(n) and e have no common divisors */
    if (err != MP_OKAY) {
	if (err == MP_UNDEF) {
	    PORT_SetError(SEC_ERROR_NEED_RANDOM);
	    err = MP_OKAY; /* to keep PORT_SetError from being called again */
	    rv = SECFailure;
	}
	goto cleanup;
    }

    /* 4.  Compute exponent1 = d mod (p-1) */
    CHECK_MPI_OK( mp_mod(d, &psub1, &tmp) );
    MPINT_TO_SECITEM(&tmp, &key->exponent1, key->arena);
    /* 5.  Compute exponent2 = d mod (q-1) */
    CHECK_MPI_OK( mp_mod(d, &qsub1, &tmp) );
    MPINT_TO_SECITEM(&tmp, &key->exponent2, key->arena);
    /* 6.  Compute coefficient = q**-1 mod p */
    CHECK_MPI_OK( mp_invmod(q, p, &tmp) );
    MPINT_TO_SECITEM(&tmp, &key->coefficient, key->arena);

    /* copy our calculated results, overwrite what is there */
    key->modulus.data = NULL;
    MPINT_TO_SECITEM(&n, &key->modulus, key->arena);
    key->privateExponent.data = NULL;
    MPINT_TO_SECITEM(d, &key->privateExponent, key->arena);
    key->publicExponent.data = NULL;
    MPINT_TO_SECITEM(e, &key->publicExponent, key->arena);
    key->prime1.data = NULL;
    MPINT_TO_SECITEM(p, &key->prime1, key->arena);
    key->prime2.data = NULL;
    MPINT_TO_SECITEM(q, &key->prime2, key->arena);
cleanup:
    mp_clear(&n);
    mp_clear(&phi);
    mp_clear(&psub1);
    mp_clear(&qsub1);
    mp_clear(&tmp);
    if (err) {
	MP_TO_SEC_ERROR(err);
	rv = SECFailure;
    }
    return rv;
}
Example #22
0
static SECStatus 
dsa_SignDigest(DSAPrivateKey *key, SECItem *signature, const SECItem *digest,
               const unsigned char *kb)
{
    mp_int p, q, g;  /* PQG parameters */
    mp_int x, k;     /* private key & pseudo-random integer */
    mp_int r, s;     /* tuple (r, s) is signature) */
    mp_err err   = MP_OKAY;
    SECStatus rv = SECSuccess;
    unsigned int dsa_subprime_len, dsa_signature_len, offset;
    SECItem localDigest;
    unsigned char localDigestData[DSA_MAX_SUBPRIME_LEN];
    

    /* FIPS-compliance dictates that digest is a SHA hash. */
    /* Check args. */
    if (!key || !signature || !digest) {
	PORT_SetError(SEC_ERROR_INVALID_ARGS);
	return SECFailure;
    }

    dsa_subprime_len = PQG_GetLength(&key->params.subPrime);
    dsa_signature_len = dsa_subprime_len*2;
    if ((signature->len < dsa_signature_len) ||
	(digest->len > HASH_LENGTH_MAX)  ||
	(digest->len < SHA1_LENGTH)) {
	PORT_SetError(SEC_ERROR_INVALID_ARGS);
	return SECFailure;
    }

    /* DSA accepts digests not equal to dsa_subprime_len, if the 
     * digests are greater, then they are truncated to the size of 
     * dsa_subprime_len, using the left most bits. If they are less
     * then they are padded on the left.*/
    PORT_Memset(localDigestData, 0, dsa_subprime_len);
    offset = (digest->len < dsa_subprime_len) ? 
			(dsa_subprime_len - digest->len) : 0;
    PORT_Memcpy(localDigestData+offset, digest->data, 
		dsa_subprime_len - offset);
    localDigest.data = localDigestData;
    localDigest.len = dsa_subprime_len;

    /* Initialize MPI integers. */
    MP_DIGITS(&p) = 0;
    MP_DIGITS(&q) = 0;
    MP_DIGITS(&g) = 0;
    MP_DIGITS(&x) = 0;
    MP_DIGITS(&k) = 0;
    MP_DIGITS(&r) = 0;
    MP_DIGITS(&s) = 0;
    CHECK_MPI_OK( mp_init(&p) );
    CHECK_MPI_OK( mp_init(&q) );
    CHECK_MPI_OK( mp_init(&g) );
    CHECK_MPI_OK( mp_init(&x) );
    CHECK_MPI_OK( mp_init(&k) );
    CHECK_MPI_OK( mp_init(&r) );
    CHECK_MPI_OK( mp_init(&s) );
    /*
    ** Convert stored PQG and private key into MPI integers.
    */
    SECITEM_TO_MPINT(key->params.prime,    &p);
    SECITEM_TO_MPINT(key->params.subPrime, &q);
    SECITEM_TO_MPINT(key->params.base,     &g);
    SECITEM_TO_MPINT(key->privateValue,    &x);
    OCTETS_TO_MPINT(kb, &k, dsa_subprime_len);
    /*
    ** FIPS 186-1, Section 5, Step 1
    **
    ** r = (g**k mod p) mod q
    */
    CHECK_MPI_OK( mp_exptmod(&g, &k, &p, &r) ); /* r = g**k mod p */
    CHECK_MPI_OK(     mp_mod(&r, &q, &r) );     /* r = r mod q    */
    /*                                  
    ** FIPS 186-1, Section 5, Step 2
    **
    ** s = (k**-1 * (HASH(M) + x*r)) mod q
    */
    SECITEM_TO_MPINT(localDigest, &s);          /* s = HASH(M)     */
    CHECK_MPI_OK( mp_invmod(&k, &q, &k) );      /* k = k**-1 mod q */
    CHECK_MPI_OK( mp_mulmod(&x, &r, &q, &x) );  /* x = x * r mod q */
    CHECK_MPI_OK( mp_addmod(&s, &x, &q, &s) );  /* s = s + x mod q */
    CHECK_MPI_OK( mp_mulmod(&s, &k, &q, &s) );  /* s = s * k mod q */
    /*
    ** verify r != 0 and s != 0
    ** mentioned as optional in FIPS 186-1.
    */
    if (mp_cmp_z(&r) == 0 || mp_cmp_z(&s) == 0) {
	PORT_SetError(SEC_ERROR_NEED_RANDOM);
	rv = SECFailure;
	goto cleanup;
    }
    /*
    ** Step 4
    **
    ** Signature is tuple (r, s)
    */
    err = mp_to_fixlen_octets(&r, signature->data, dsa_subprime_len);
    if (err < 0) goto cleanup; 
    err = mp_to_fixlen_octets(&s, signature->data + dsa_subprime_len, 
                                  dsa_subprime_len);
    if (err < 0) goto cleanup; 
    err = MP_OKAY;
    signature->len = dsa_signature_len;
cleanup:
    PORT_Memset(localDigestData, 0, DSA_MAX_SUBPRIME_LEN);
    mp_clear(&p);
    mp_clear(&q);
    mp_clear(&g);
    mp_clear(&x);
    mp_clear(&k);
    mp_clear(&r);
    mp_clear(&s);
    if (err) {
	translate_mpi_error(err);
	rv = SECFailure;
    }
    return rv;
}
Example #23
0
/* Reduces an integer to a field element. */
mp_err
ec_GFp_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
{
    return mp_mod(a, &meth->irr, r);
}
Example #24
0
/* signature is caller-supplied buffer of at least 20 bytes.
** On input,  signature->len == size of buffer to hold signature.
**            digest->len    == size of digest.
*/
SECStatus 
DSA_VerifyDigest(DSAPublicKey *key, const SECItem *signature, 
                 const SECItem *digest)
{
    /* FIPS-compliance dictates that digest is a SHA hash. */
    mp_int p, q, g;      /* PQG parameters */
    mp_int r_, s_;       /* tuple (r', s') is received signature) */
    mp_int u1, u2, v, w; /* intermediate values used in verification */
    mp_int y;            /* public key */
    mp_err err;
    int dsa_subprime_len, dsa_signature_len, offset;
    SECItem localDigest;
    unsigned char localDigestData[DSA_MAX_SUBPRIME_LEN];
    SECStatus verified = SECFailure;

    /* Check args. */
    if (!key || !signature || !digest ) {
	PORT_SetError(SEC_ERROR_INVALID_ARGS);
	return SECFailure;
    }

    dsa_subprime_len = PQG_GetLength(&key->params.subPrime);
    dsa_signature_len = dsa_subprime_len*2;
    if ((signature->len != dsa_signature_len) ||
	(digest->len > HASH_LENGTH_MAX)  ||
	(digest->len < SHA1_LENGTH)) {
	PORT_SetError(SEC_ERROR_INVALID_ARGS);
	return SECFailure;
    }

    /* DSA accepts digests not equal to dsa_subprime_len, if the 
     * digests are greater, than they are truncated to the size of 
     * dsa_subprime_len, using the left most bits. If they are less
     * then they are padded on the left.*/
    PORT_Memset(localDigestData, 0, dsa_subprime_len);
    offset = (digest->len < dsa_subprime_len) ? 
			(dsa_subprime_len - digest->len) : 0;
    PORT_Memcpy(localDigestData+offset, digest->data, 
		dsa_subprime_len - offset);
    localDigest.data = localDigestData;
    localDigest.len = dsa_subprime_len;

    /* Initialize MPI integers. */
    MP_DIGITS(&p)  = 0;
    MP_DIGITS(&q)  = 0;
    MP_DIGITS(&g)  = 0;
    MP_DIGITS(&y)  = 0;
    MP_DIGITS(&r_) = 0;
    MP_DIGITS(&s_) = 0;
    MP_DIGITS(&u1) = 0;
    MP_DIGITS(&u2) = 0;
    MP_DIGITS(&v)  = 0;
    MP_DIGITS(&w)  = 0;
    CHECK_MPI_OK( mp_init(&p)  );
    CHECK_MPI_OK( mp_init(&q)  );
    CHECK_MPI_OK( mp_init(&g)  );
    CHECK_MPI_OK( mp_init(&y)  );
    CHECK_MPI_OK( mp_init(&r_) );
    CHECK_MPI_OK( mp_init(&s_) );
    CHECK_MPI_OK( mp_init(&u1) );
    CHECK_MPI_OK( mp_init(&u2) );
    CHECK_MPI_OK( mp_init(&v)  );
    CHECK_MPI_OK( mp_init(&w)  );
    /*
    ** Convert stored PQG and public key into MPI integers.
    */
    SECITEM_TO_MPINT(key->params.prime,    &p);
    SECITEM_TO_MPINT(key->params.subPrime, &q);
    SECITEM_TO_MPINT(key->params.base,     &g);
    SECITEM_TO_MPINT(key->publicValue,     &y);
    /*
    ** Convert received signature (r', s') into MPI integers.
    */
    OCTETS_TO_MPINT(signature->data, &r_, dsa_subprime_len);
    OCTETS_TO_MPINT(signature->data + dsa_subprime_len, &s_, dsa_subprime_len);
    /*
    ** Verify that 0 < r' < q and 0 < s' < q
    */
    if (mp_cmp_z(&r_) <= 0 || mp_cmp_z(&s_) <= 0 ||
        mp_cmp(&r_, &q) >= 0 || mp_cmp(&s_, &q) >= 0) {
	/* err is zero here. */
	PORT_SetError(SEC_ERROR_BAD_SIGNATURE);
	goto cleanup; /* will return verified == SECFailure */
    }
    /*
    ** FIPS 186-1, Section 6, Step 1
    **
    ** w = (s')**-1 mod q
    */
    CHECK_MPI_OK( mp_invmod(&s_, &q, &w) );      /* w = (s')**-1 mod q */
    /*
    ** FIPS 186-1, Section 6, Step 2
    **
    ** u1 = ((Hash(M')) * w) mod q
    */
    SECITEM_TO_MPINT(localDigest, &u1);              /* u1 = HASH(M')     */
    CHECK_MPI_OK( mp_mulmod(&u1, &w, &q, &u1) ); /* u1 = u1 * w mod q */
    /*
    ** FIPS 186-1, Section 6, Step 3
    **
    ** u2 = ((r') * w) mod q
    */
    CHECK_MPI_OK( mp_mulmod(&r_, &w, &q, &u2) );
    /*
    ** FIPS 186-1, Section 6, Step 4
    **
    ** v = ((g**u1 * y**u2) mod p) mod q
    */
    CHECK_MPI_OK( mp_exptmod(&g, &u1, &p, &g) ); /* g = g**u1 mod p */
    CHECK_MPI_OK( mp_exptmod(&y, &u2, &p, &y) ); /* y = y**u2 mod p */
    CHECK_MPI_OK(  mp_mulmod(&g, &y, &p, &v)  ); /* v = g * y mod p */
    CHECK_MPI_OK(     mp_mod(&v, &q, &v)      ); /* v = v mod q     */
    /*
    ** Verification:  v == r'
    */
    if (mp_cmp(&v, &r_)) {
	PORT_SetError(SEC_ERROR_BAD_SIGNATURE);
	verified = SECFailure; /* Signature failed to verify. */
    } else {
	verified = SECSuccess; /* Signature verified. */
    }
cleanup:
    mp_clear(&p);
    mp_clear(&q);
    mp_clear(&g);
    mp_clear(&y);
    mp_clear(&r_);
    mp_clear(&s_);
    mp_clear(&u1);
    mp_clear(&u2);
    mp_clear(&v);
    mp_clear(&w);
    if (err) {
	translate_mpi_error(err);
    }
    return verified;
}
Example #25
0
/* computes the modular inverse via binary extended euclidean algorithm, 
 * that is c = 1/a mod b 
 *
 * Based on slow invmod except this is optimized for the case where b is 
 * odd as per HAC Note 14.64 on pp. 610
 */
int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, B, D;
  int     res, neg;

  /* 2. [modified] b must be odd   */
  if (mp_iseven (b) == 1) {
    return MP_VAL;
  }

  /* init all our temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
     return res;
  }

  /* x == modulus, y == value to invert */
  if ((res = mp_copy (b, &x)) != MP_OKAY) {
    goto LBL_ERR;
  }

  /* we need y = |a| */
  if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
    goto LBL_ERR;
  }

  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
    goto LBL_ERR;
  }
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
    goto LBL_ERR;
  }
  mp_set (&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven (&u) == 1) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if B is odd then */
    if (mp_isodd (&B) == 1) {
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* B = B/2 */
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven (&v) == 1) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if D is odd then */
    if (mp_isodd (&D) == 1) {
      /* D = (D-x)/2 */
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* D = D/2 */
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 6.  if u >= v then */
  if (mp_cmp (&u, &v) != MP_LT) {
    /* u = u - v, B = B - D */
    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  } else {
    /* v - v - u, D = D - B */
    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero (&u) == 0) {
    goto top;
  }

  /* now a = C, b = D, gcd == g*v */

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
    res = MP_VAL;
    goto LBL_ERR;
  }

  /* b is now the inverse */
  neg = a->sign;
  while (D.sign == MP_NEG) {
    if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }
  mp_exch (&D, c);
  c->sign = neg;
  res = MP_OKAY;

LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
  return res;
}
Example #26
0
int ecc_make_key_ex(prng_state *prng, int wprng, ecc_key *key, const ltc_ecc_set_type *dp)
{
   int            err;
   ecc_point     *base;
   void          *prime, *order;
   unsigned char *buf;
   int            keysize;

   LTC_ARGCHK(key         != NULL);
   LTC_ARGCHK(ltc_mp.name != NULL);
   LTC_ARGCHK(dp          != NULL);

   /* good prng? */
   if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
      return err;
   }

   key->idx = -1;
   key->dp  = dp;
   keysize  = dp->size;

   /* allocate ram */
   base = NULL;
   buf  = XMALLOC(ECC_MAXSIZE);
   if (buf == NULL) {
      return CRYPT_MEM;
   }

   /* make up random string */
   if (prng_descriptor[wprng].read(buf, (unsigned long)keysize, prng) != (unsigned long)keysize) {
      err = CRYPT_ERROR_READPRNG;
      goto ERR_BUF;
   }

   /* setup the key variables */
   if ((err = mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->pubkey.z, &key->k, &prime, &order, NULL)) != CRYPT_OK) {
      goto ERR_BUF;
   }
   base = ltc_ecc_new_point();
   if (base == NULL) {
      err = CRYPT_MEM;
      goto errkey;
   }

   /* read in the specs for this key */
   if ((err = mp_read_radix(prime,   (char *)key->dp->prime, 16)) != CRYPT_OK)                  { goto errkey; }
   if ((err = mp_read_radix(order,   (char *)key->dp->order, 16)) != CRYPT_OK)                  { goto errkey; }
   if ((err = mp_read_radix(base->x, (char *)key->dp->Gx, 16)) != CRYPT_OK)                     { goto errkey; }
   if ((err = mp_read_radix(base->y, (char *)key->dp->Gy, 16)) != CRYPT_OK)                     { goto errkey; }
   if ((err = mp_set(base->z, 1)) != CRYPT_OK)                                                  { goto errkey; }
   if ((err = mp_read_unsigned_bin(key->k, (unsigned char *)buf, keysize)) != CRYPT_OK)         { goto errkey; }

   /* the key should be smaller than the order of base point */
   if (mp_cmp(key->k, order) != LTC_MP_LT) {
       if((err = mp_mod(key->k, order, key->k)) != CRYPT_OK)                                    { goto errkey; }
   }
   /* make the public key */
   if ((err = ltc_mp.ecc_ptmul(key->k, base, &key->pubkey, prime, 1)) != CRYPT_OK)              { goto errkey; }
   key->type = PK_PRIVATE;

   /* free up ram */
   err = CRYPT_OK;
   goto cleanup;
errkey:
   mp_clear_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z, key->k, NULL);
cleanup:
   ltc_ecc_del_point(base);
   mp_clear_multi(prime, order, NULL);
ERR_BUF:
#ifdef LTC_CLEAN_STACK
   zeromem(buf, ECC_MAXSIZE);
#endif
   XFREE(buf);
   return err;
}
Example #27
0
SECStatus
RSA_PrivateKeyCheck(RSAPrivateKey *key)
{
    mp_int p, q, n, psub1, qsub1, e, d, d_p, d_q, qInv, res;
    mp_err   err = MP_OKAY;
    SECStatus rv = SECSuccess;
    MP_DIGITS(&n)    = 0;
    MP_DIGITS(&psub1)= 0;
    MP_DIGITS(&qsub1)= 0;
    MP_DIGITS(&e)    = 0;
    MP_DIGITS(&d)    = 0;
    MP_DIGITS(&d_p)  = 0;
    MP_DIGITS(&d_q)  = 0;
    MP_DIGITS(&qInv) = 0;
    MP_DIGITS(&res)  = 0;
    CHECK_MPI_OK( mp_init(&n)    );
    CHECK_MPI_OK( mp_init(&p)    );
    CHECK_MPI_OK( mp_init(&q)    );
    CHECK_MPI_OK( mp_init(&psub1));
    CHECK_MPI_OK( mp_init(&qsub1));
    CHECK_MPI_OK( mp_init(&e)    );
    CHECK_MPI_OK( mp_init(&d)    );
    CHECK_MPI_OK( mp_init(&d_p)  );
    CHECK_MPI_OK( mp_init(&d_q)  );
    CHECK_MPI_OK( mp_init(&qInv) );
    CHECK_MPI_OK( mp_init(&res)  );
    SECITEM_TO_MPINT(key->modulus,         &n);
    SECITEM_TO_MPINT(key->prime1,          &p);
    SECITEM_TO_MPINT(key->prime2,          &q);
    SECITEM_TO_MPINT(key->publicExponent,  &e);
    SECITEM_TO_MPINT(key->privateExponent, &d);
    SECITEM_TO_MPINT(key->exponent1,       &d_p);
    SECITEM_TO_MPINT(key->exponent2,       &d_q);
    SECITEM_TO_MPINT(key->coefficient,     &qInv);
    /* p > q  */
    if (mp_cmp(&p, &q) <= 0) {
	/* mind the p's and q's (and d_p's and d_q's) */
	SECItem tmp;
	mp_exch(&p, &q);
	mp_exch(&d_p,&d_q);
	tmp = key->prime1;
	key->prime1 = key->prime2;
	key->prime2 = tmp;
	tmp = key->exponent1;
	key->exponent1 = key->exponent2;
	key->exponent2 = tmp;
    }
#define VERIFY_MPI_EQUAL(m1, m2) \
    if (mp_cmp(m1, m2) != 0) {   \
	rv = SECFailure;         \
	goto cleanup;            \
    }
#define VERIFY_MPI_EQUAL_1(m)    \
    if (mp_cmp_d(m, 1) != 0) {   \
	rv = SECFailure;         \
	goto cleanup;            \
    }
    /*
     * The following errors cannot be recovered from.
     */
    /* n == p * q */
    CHECK_MPI_OK( mp_mul(&p, &q, &res) );
    VERIFY_MPI_EQUAL(&res, &n);
    /* gcd(e, p-1) == 1 */
    CHECK_MPI_OK( mp_sub_d(&p, 1, &psub1) );
    CHECK_MPI_OK( mp_gcd(&e, &psub1, &res) );
    VERIFY_MPI_EQUAL_1(&res);
    /* gcd(e, q-1) == 1 */
    CHECK_MPI_OK( mp_sub_d(&q, 1, &qsub1) );
    CHECK_MPI_OK( mp_gcd(&e, &qsub1, &res) );
    VERIFY_MPI_EQUAL_1(&res);
    /* d*e == 1 mod p-1 */
    CHECK_MPI_OK( mp_mulmod(&d, &e, &psub1, &res) );
    VERIFY_MPI_EQUAL_1(&res);
    /* d*e == 1 mod q-1 */
    CHECK_MPI_OK( mp_mulmod(&d, &e, &qsub1, &res) );
    VERIFY_MPI_EQUAL_1(&res);
    /*
     * The following errors can be recovered from.
     */
    /* d_p == d mod p-1 */
    CHECK_MPI_OK( mp_mod(&d, &psub1, &res) );
    if (mp_cmp(&d_p, &res) != 0) {
	/* swap in the correct value */
	CHECK_SEC_OK( swap_in_key_value(key->arena, &res, &key->exponent1) );
    }
    /* d_q == d mod q-1 */
    CHECK_MPI_OK( mp_mod(&d, &qsub1, &res) );
    if (mp_cmp(&d_q, &res) != 0) {
	/* swap in the correct value */
	CHECK_SEC_OK( swap_in_key_value(key->arena, &res, &key->exponent2) );
    }
    /* q * q**-1 == 1 mod p */
    CHECK_MPI_OK( mp_mulmod(&q, &qInv, &p, &res) );
    if (mp_cmp_d(&res, 1) != 0) {
	/* compute the correct value */
	CHECK_MPI_OK( mp_invmod(&q, &p, &qInv) );
	CHECK_SEC_OK( swap_in_key_value(key->arena, &qInv, &key->coefficient) );
    }
cleanup:
    mp_clear(&n);
    mp_clear(&p);
    mp_clear(&q);
    mp_clear(&psub1);
    mp_clear(&qsub1);
    mp_clear(&e);
    mp_clear(&d);
    mp_clear(&d_p);
    mp_clear(&d_q);
    mp_clear(&qInv);
    mp_clear(&res);
    if (err) {
	MP_TO_SEC_ERROR(err);
	rv = SECFailure;
    }
    return rv;
}
Example #28
0
/** 
   Create a Katja key
   @param prng     An active PRNG state
   @param wprng    The index of the PRNG desired
   @param size     The size of the modulus (key size) desired (octets)
   @param key      [out] Destination of a newly created private key pair
   @return CRYPT_OK if successful, upon error all allocated ram is freed
*/
int katja_make_key(prng_state *prng, int wprng, int size, katja_key *key)
{
   void *p, *q, *tmp1, *tmp2;
   int    err;
  
   LTC_ARGCHK(key != NULL);
   LTC_ARGCHK(ltc_mp.name != NULL);

   if ((size < (MIN_KAT_SIZE/8)) || (size > (MAX_KAT_SIZE/8))) {
      return CRYPT_INVALID_KEYSIZE;
   }

   if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
      return err;
   }

   if ((err = mp_init_multi(&p, &q, &tmp1, &tmp2, NULL)) != CRYPT_OK) {
      return err;
   }

   /* divide size by three  */
   size   = (((size << 3) / 3) + 7) >> 3;

   /* make prime "q" (we negate size to make q == 3 mod 4) */
   if ((err = rand_prime(q, -size, prng, wprng)) != CRYPT_OK)      { goto done; }
   if ((err = mp_sub_d(q, 1, tmp1)) != CRYPT_OK)                   { goto done; }

   /* make prime "p" */
   do {
      if ((err = rand_prime(p, size+1, prng, wprng)) != CRYPT_OK)  { goto done; }
      if ((err = mp_gcd(p, tmp1, tmp2)) != CRYPT_OK)               { goto done; }
   } while (mp_cmp_d(tmp2, 1) != LTC_MP_EQ);

   /* make key */
   if ((err = mp_init_multi(&key->d, &key->N, &key->dQ, &key->dP,
                     &key->qP, &key->p, &key->q, &key->pq, NULL)) != CRYPT_OK) {
      goto error;
   }

   /* n=p^2q and 1/n mod pq */
   if ((err = mp_copy( p,  key->p)) != CRYPT_OK)                       { goto error2; }
   if ((err = mp_copy( q,  key->q)) != CRYPT_OK)                       { goto error2; }
   if ((err = mp_mul(key->p, key->q, key->pq)) != CRYPT_OK)            { goto error2; } /* tmp1 = pq  */
   if ((err = mp_mul(key->pq, key->p, key->N)) != CRYPT_OK)            { goto error2; } /* N = p^2q   */  
   if ((err = mp_sub_d( p, 1,  tmp1)) != CRYPT_OK)                     { goto error2; } /* tmp1 = q-1 */
   if ((err = mp_sub_d( q, 1,  tmp2)) != CRYPT_OK)                     { goto error2; } /* tmp2 = p-1 */
   if ((err = mp_lcm(tmp1, tmp2, key->d)) != CRYPT_OK)                 { goto error2; } /* tmp1 = lcd(p-1,q-1) */
   if ((err = mp_invmod( key->N,  key->d,  key->d)) != CRYPT_OK)       { goto error2; } /* key->d = 1/N mod pq */

   /* optimize for CRT now */
   /* find d mod q-1 and d mod p-1 */
   if ((err = mp_mod( key->d,  tmp1,  key->dP)) != CRYPT_OK)           { goto error2; } /* dP = d mod p-1 */
   if ((err = mp_mod( key->d,  tmp2,  key->dQ)) != CRYPT_OK)           { goto error2; } /* dQ = d mod q-1 */
   if ((err = mp_invmod( q,  p,  key->qP)) != CRYPT_OK)                { goto error2; } /* qP = 1/q mod p */

   /* set key type (in this case it's CRT optimized) */
   key->type = PK_PRIVATE;

   /* return ok and free temps */
   err       = CRYPT_OK;
   goto done;
error2:
   mp_clear_multi( key->d,  key->N,  key->dQ,  key->dP,  key->qP,  key->p,  key->q, key->pq, NULL);
error:
done:
   mp_clear_multi( tmp2,  tmp1,  p,  q, NULL);
   return err;
}