/* d = a * b (mod c) */
int mp_mulmod_montgomery (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
int res;
mp_int R;
mp_digit mp;
/* initialize R */
if ((res = mp_init(&R)) != MP_OKAY) {
printf("Error initializing the number. %s", mp_error_to_string(res));
return EXIT_FAILURE;
}
/* get normalizzation */
if ((res = mp_montgomery_calc_normalization(&R,c)) != MP_OKAY) {
printf("Error getting norm. %s", mp_error_to_string(res));
return EXIT_FAILURE;
}
/* get mp value */
if ((res = mp_montgomery_setup(c, &mp)) != MP_OKAY) {
printf("Error setting up montgomery. %s", mp_error_to_string(res));
return EXIT_FAILURE;
}
/* normalize ‘a’ so now a is equal to aR */
if ((res = mp_mulmod(a, &R, c, a)) != MP_OKAY) {
printf("Error computing aR. %s", mp_error_to_string(res));
return EXIT_FAILURE;
}
/* normalize ‘b’ so now a is equal to bR */
if ((res = mp_mulmod(b, &R, c, b)) != MP_OKAY) {
printf("Error computing aR. %s", mp_error_to_string(res));
return EXIT_FAILURE;
}
/* compute a * b in Montgomery domain */
if ((res = mp_mul(a, b, d)) != MP_OKAY) {
printf("Error multiplying. %s", mp_error_to_string(res));
return EXIT_FAILURE;
}
/* now reduce ‘d’ back down to d = a*b*R^2 * R^-1 == a*b*R */
if ((res = mp_montgomery_reduce(d, c, mp)) != MP_OKAY) {
printf("Error reducing. %s", mp_error_to_string(res));
return EXIT_FAILURE;
}
/* now reduce ‘d’ back down to d = a*b*R * R^-1 == a*b */
if ((res = mp_montgomery_reduce(d, c, mp)) != MP_OKAY) {
printf("Error reducing. %s", mp_error_to_string(res));
return EXIT_FAILURE;
}
mp_clear (&R);
return res;
}
int main(void)
{
mp_int modulus, R, p, pp;
mp_digit mp;
long x, y;
srand(time(NULL));
mp_init_multi(&modulus, &R, &p, &pp, NULL);
/* loop through various sizes */
for (x = 4; x < 256; x++) {
printf("DIGITS == %3ld...", x); fflush(stdout);
/* make up the odd modulus */
mp_rand(&modulus, x);
modulus.dp[0] |= 1;
/* now find the R value */
mp_montgomery_calc_normalization(&R, &modulus);
mp_montgomery_setup(&modulus, &mp);
/* now run through a bunch tests */
for (y = 0; y < 1000; y++) {
mp_rand(&p, x/2); /* p = random */
mp_mul(&p, &R, &pp); /* pp = R * p */
mp_montgomery_reduce(&pp, &modulus, mp);
/* should be equal to p */
if (mp_cmp(&pp, &p) != MP_EQ) {
printf("FAILURE!\n");
exit(-1);
}
}
printf("PASSED\n");
}
return 0;
}
int mp_exptmod_fast (mp_int * G, mp_int * X, 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*,mp_int*,mp_digit);
/* 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) < 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, 1);
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[1 << (winsize - 1)])) != MP_OKAY) {
goto LBL_RES;
}
for (x = 0; x < (winsize - 1); x++) {
if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
goto LBL_RES;
}
if ((err = redux (&M[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;
}
/* get normalization value */
static int montgomery_normalization(void *a, void *b)
{
LTC_ARGCHK(a != NULL);
LTC_ARGCHK(b != NULL);
return mpi_to_ltc_error(mp_montgomery_calc_normalization(a, b));
}
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_digit mp;
mp_init(&a);
mp_init(&b);
mp_init(&c);
mp_init(&d);
mp_init(&e);
mp_init(&f);
srand(time(NULL));
#if 0
// test montgomery
printf("Testing montgomery...\n");
for (i = 1; i < 10; i++) {
printf("Testing digit size: %d\n", i);
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"); exit(EXIT_FAILURE); }
}
}
}
printf("done\n");
// 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 < 128; 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 < 128; 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, 2);
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
/* test the mp_reduce_2k_l code */
#if 0
#if 0
/* 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 1
/* 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);
#endif
mp_todecimal(&a, buf);
printf("p==%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 < (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 %lu\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
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);
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;
}
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;
}