int fp3_srt(fp3_t c, fp3_t a) {
int r = 0;
fp3_t t0, t1, t2, t3;
bn_t e;
fp3_null(t0);
fp3_null(t1);
fp3_null(t2);
fp3_null(t3);
bn_null(e);
TRY {
fp3_new(t0);
fp3_new(t1);
fp3_new(t2);
fp3_new(t3);
bn_new(e);
fp3_dbl(t3, a);
fp3_frb(t0, t3, 1);
fp3_sqr(t1, t0);
fp3_mul(t2, t1, t0);
fp3_mul(t1, t1, t2);
fp3_frb(t0, t0, 1);
fp3_mul(t3, t3, t1);
fp3_mul(t0, t0, t3);
e->used = FP_DIGS;
dv_copy(e->dp, fp_prime_get(), FP_DIGS);
bn_sub_dig(e, e, 5);
bn_div_dig(e, e, 8);
fp3_exp(t0, t0, e);
fp3_mul(t0, t0, t2);
fp3_sqr(t1, t0);
fp3_mul(t1, t1, a);
fp3_dbl(t1, t1);
fp3_mul(t0, t0, a);
fp_sub_dig(t1[0], t1[0], 1);
fp3_mul(c, t0, t1);
fp3_sqr(t0, c);
if (fp3_cmp(t0, a) == CMP_EQ) {
r = 1;
}
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp3_free(t0);
fp3_free(t1);
fp3_free(t2);
fp3_free(t3);
bn_free(e);
}
return r;
}
int cp_bdpe_dec(dig_t *out, uint8_t *in, int in_len, bdpe_t prv) {
bn_t m, t, z;
unsigned i;
int size, result = STS_OK;
size = bn_size_bin(prv->n);
if (in_len < 0 || in_len != size) {
return STS_ERR;
}
bn_null(m);
bn_null(t);
bn_null(z);
TRY {
bn_new(m);
bn_new(t);
bn_new(z);
/* Compute t = (p-1)(q-1)/block. */
bn_mul(t, prv->p, prv->q);
bn_sub(t, t, prv->p);
bn_sub(t, t, prv->q);
bn_add_dig(t, t, 1);
bn_div_dig(t, t, prv->t);
bn_read_bin(m, in, in_len);
bn_mxp(m, m, t, prv->n);
bn_mxp(t, prv->y, t, prv->n);
for (i = 0; i < prv->t; i++) {
bn_mxp_dig(z, t, i, prv->n);
if (bn_cmp(z, m) == CMP_EQ) {
*out = i;
break;
}
}
if (i == prv->t) {
result = STS_ERR;
}
} CATCH_ANY {
result = STS_ERR;
}
FINALLY {
bn_free(m);
bn_free(t);
bn_free(z);
}
return result;
}
int bn_size_str(const bn_t a, int radix) {
int digits = 0;
bn_t t;
bn_null(t);
/* Binary case requires the bits, a sign and the null terminator. */
if (radix == 2) {
return bn_bits(a) + (a->sign == BN_NEG ? 1 : 0) + 1;
}
/* Check the radix. */
if (radix < 2 || radix > 64) {
THROW(ERR_NO_VALID);
}
if (bn_is_zero(a)) {
return 2;
}
if (a->sign == BN_NEG) {
digits++;
}
TRY {
bn_new(t);
bn_copy(t, a);
t->sign = BN_POS;
while (!bn_is_zero(t)) {
bn_div_dig(t, t, (dig_t)radix);
digits++;
}
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
bn_free(t);
}
return digits + 1;
}
int cp_bdpe_gen(bdpe_t pub, bdpe_t prv, dig_t block, int bits) {
bn_t t, r;
int result = STS_OK;
bn_null(t);
bn_null(r);
TRY {
bn_new(t);
bn_new(r);
prv->t = pub->t = block;
/* Make sure that block size is prime. */
bn_set_dig(t, block);
if (bn_is_prime_basic(t) == 0) {
THROW(ERR_NO_VALID);
}
/* Generate prime q such that gcd(block, (q - 1)) = 1. */
do {
bn_gen_prime(prv->q, bits / 2);
bn_sub_dig(prv->q, prv->q, 1);
bn_gcd_dig(t, prv->q, block);
bn_add_dig(prv->q, prv->q, 1);
} while (bn_cmp_dig(t, 1) != CMP_EQ);
/* Generate different primes p and q. */
do {
/* Compute p = block * (x * block + b) + 1, 0 < b < block random. */
bn_rand(prv->p, BN_POS, bits / 2 - 2 * util_bits_dig(block));
bn_mul_dig(prv->p, prv->p, block);
bn_rand(t, BN_POS, util_bits_dig(block));
bn_add_dig(prv->p, prv->p, t->dp[0]);
/* We know that block divides (p-1). */
bn_gcd_dig(t, prv->p, block);
bn_mul_dig(prv->p, prv->p, block);
bn_add_dig(prv->p, prv->p, 1);
} while (bn_cmp_dig(t, 1) != CMP_EQ || bn_is_prime(prv->p) == 0);
/* Compute t = (p-1)*(q-1). */
bn_sub_dig(prv->q, prv->q, 1);
bn_sub_dig(prv->p, prv->p, 1);
bn_mul(t, prv->p, prv->q);
bn_div_dig(t, t, block);
/* Restore factors p and q and compute n = p * q. */
bn_add_dig(prv->p, prv->p, 1);
bn_add_dig(prv->q, prv->q, 1);
bn_mul(pub->n, prv->p, prv->q);
bn_copy(prv->n, pub->n);
/* Select random y such that y^{(p-1)(q-1)}/block \neq 1 mod N. */
do {
bn_rand(pub->y, BN_POS, bits);
bn_mxp(r, pub->y, t, pub->n);
} while (bn_cmp_dig(r, 1) == CMP_EQ);
bn_copy(prv->y, pub->y);
}
CATCH_ANY {
result = STS_ERR;
}
FINALLY {
bn_free(t);
bn_free(r);
}
return result;
}
/**
* Computes the constants required for evaluating Frobenius maps.
*/
static void fp3_calc() {
bn_t e;
fp3_t t0, t1, t2;
ctx_t *ctx = core_get();
bn_null(e);
fp3_null(t0);
fp3_null(t1);
fp3_null(t2);
TRY {
bn_new(e);
fp3_new(t0);
fp3_new(t1);
fp3_new(t2);
fp_set_dig(ctx->fp3_base[0], -fp_prime_get_cnr());
fp_neg(ctx->fp3_base[0], ctx->fp3_base[0]);
e->used = FP_DIGS;
dv_copy(e->dp, fp_prime_get(), FP_DIGS);
bn_sub_dig(e, e, 1);
bn_div_dig(e, e, 3);
fp_exp(ctx->fp3_base[0], ctx->fp3_base[0], e);
fp_sqr(ctx->fp3_base[1], ctx->fp3_base[0]);
fp3_zero(t0);
fp_set_dig(t0[1], 1);
dv_copy(e->dp, fp_prime_get(), FP_DIGS);
bn_sub_dig(e, e, 1);
bn_div_dig(e, e, 6);
/* t0 = u^((p-1)/6). */
fp3_exp(t0, t0, e);
fp_copy(ctx->fp3_p[0], t0[2]);
fp3_sqr(t1, t0);
fp_copy(ctx->fp3_p[1], t1[1]);
fp3_mul(t2, t1, t0);
fp_copy(ctx->fp3_p[2], t2[0]);
fp3_sqr(t2, t1);
fp_copy(ctx->fp3_p[3], t2[2]);
fp3_mul(t2, t2, t0);
fp_copy(ctx->fp3_p[4], t2[1]);
fp_mul(ctx->fp3_p2[0], ctx->fp3_p[0], ctx->fp3_base[1]);
fp_mul(t0[0], ctx->fp3_p2[0], ctx->fp3_p[0]);
fp_neg(ctx->fp3_p2[0], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p2[0], ctx->fp3_p2[0], t0[0]);
}
fp_mul(ctx->fp3_p2[1], ctx->fp3_p[1], ctx->fp3_base[0]);
fp_mul(ctx->fp3_p2[1], ctx->fp3_p2[1], ctx->fp3_p[1]);
fp_sqr(ctx->fp3_p2[2], ctx->fp3_p[2]);
fp_mul(ctx->fp3_p2[3], ctx->fp3_p[3], ctx->fp3_base[1]);
fp_mul(t0[0], ctx->fp3_p2[3], ctx->fp3_p[3]);
fp_neg(ctx->fp3_p2[3], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p2[3], ctx->fp3_p2[3], t0[0]);
}
fp_mul(ctx->fp3_p2[4], ctx->fp3_p[4], ctx->fp3_base[0]);
fp_mul(ctx->fp3_p2[4], ctx->fp3_p2[4], ctx->fp3_p[4]);
fp_mul(ctx->fp3_p3[0], ctx->fp3_p[0], ctx->fp3_base[0]);
fp_mul(t0[0], ctx->fp3_p3[0], ctx->fp3_p2[0]);
fp_neg(ctx->fp3_p3[0], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p3[0], ctx->fp3_p3[0], t0[0]);
}
fp_mul(ctx->fp3_p3[1], ctx->fp3_p[1], ctx->fp3_base[1]);
fp_mul(t0[0], ctx->fp3_p3[1], ctx->fp3_p2[1]);
fp_neg(ctx->fp3_p3[1], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p3[1], ctx->fp3_p3[1], t0[0]);
}
fp_mul(ctx->fp3_p3[2], ctx->fp3_p[2], ctx->fp3_p2[2]);
fp_mul(ctx->fp3_p3[3], ctx->fp3_p[3], ctx->fp3_base[0]);
fp_mul(t0[0], ctx->fp3_p3[3], ctx->fp3_p2[3]);
fp_neg(ctx->fp3_p3[3], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p3[3], ctx->fp3_p3[3], t0[0]);
}
fp_mul(ctx->fp3_p3[4], ctx->fp3_p[4], ctx->fp3_base[1]);
fp_mul(t0[0], ctx->fp3_p3[4], ctx->fp3_p2[4]);
fp_neg(ctx->fp3_p3[4], t0[0]);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_sub(ctx->fp3_p3[4], ctx->fp3_p3[4], t0[0]);
}
for (int i = 0; i < 5; i++) {
fp_mul(ctx->fp3_p4[i], ctx->fp3_p[i], ctx->fp3_p3[i]);
fp_mul(ctx->fp3_p5[i], ctx->fp3_p2[i], ctx->fp3_p3[i]);
}
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
bn_free(e);
fp3_free(t0);
fp3_free(t1);
fp3_free(t2);
}
}
/**
* Computes the constantes required for evaluating Frobenius maps.
*/
static void fp2_calc() {
bn_t e;
fp2_t t0;
fp2_t t1;
ctx_t *ctx = core_get();
bn_null(e);
fp2_null(t0);
fp2_null(t1);
TRY {
bn_new(e);
fp2_new(t0);
fp2_new(t1);
fp2_zero(t0);
fp_set_dig(t0[0], 1);
fp2_mul_nor(t0, t0);
e->used = FP_DIGS;
dv_copy(e->dp, fp_prime_get(), FP_DIGS);
bn_sub_dig(e, e, 1);
bn_div_dig(e, e, 6);
fp2_exp(t0, t0, e);
#if ALLOC == AUTO
fp2_copy(ctx->fp2_p[0], t0);
fp2_sqr(ctx->fp2_p[1], ctx->fp2_p[0]);
fp2_mul(ctx->fp2_p[2], ctx->fp2_p[1], ctx->fp2_p[0]);
fp2_sqr(ctx->fp2_p[3], ctx->fp2_p[1]);
fp2_mul(ctx->fp2_p[4], ctx->fp2_p[3], ctx->fp2_p[0]);
#else
fp_copy(ctx->fp2_p[0][0], t0[0]);
fp_copy(ctx->fp2_p[0][1], t0[1]);
fp2_sqr(t1, t0);
fp_copy(ctx->fp2_p[1][0], t1[0]);
fp_copy(ctx->fp2_p[1][1], t1[1]);
fp2_mul(t1, t1, t0);
fp_copy(ctx->fp2_p[2][0], t1[0]);
fp_copy(ctx->fp2_p[2][1], t1[1]);
fp2_sqr(t1, t0);
fp2_sqr(t1, t1);
fp_copy(ctx->fp2_p[3][0], t1[0]);
fp_copy(ctx->fp2_p[3][1], t1[1]);
fp2_mul(t1, t1, t0);
fp_copy(ctx->fp2_p[4][0], t1[0]);
fp_copy(ctx->fp2_p[4][1], t1[1]);
#endif
fp2_frb(t1, t0, 1);
fp2_mul(t0, t1, t0);
fp_copy(ctx->fp2_p2[0], t0[0]);
fp_sqr(ctx->fp2_p2[1], ctx->fp2_p2[0]);
fp_mul(ctx->fp2_p2[2], ctx->fp2_p2[1], ctx->fp2_p2[0]);
fp_sqr(ctx->fp2_p2[3], ctx->fp2_p2[1]);
for (int i = 0; i < 5; i++) {
fp_mul(ctx->fp2_p3[i][0], ctx->fp2_p2[i % 3], ctx->fp2_p[i][0]);
fp_mul(ctx->fp2_p3[i][1], ctx->fp2_p2[i % 3], ctx->fp2_p[i][1]);
}
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
bn_free(e);
fp2_free(t0);
fp2_free(t1);
}
}
void fp_param_set(int param) {
bn_t t0, t1, t2, p;
int f[10] = { 0 };
bn_null(t0);
bn_null(t1);
bn_null(t2);
bn_null(p);
/* Suppress possible unused parameter warning. */
(void) f;
TRY {
bn_new(t0);
bn_new(t1);
bn_new(t2);
bn_new(p);
core_get()->fp_id = param;
switch (param) {
#if FP_PRIME == 158
case BN_158:
/* x = 4000000031. */
fp_param_get_var(t0);
/* p = 36 * x^4 + 36 * x^3 + 24 * x^2 + 6 * x + 1. */
bn_set_dig(p, 1);
bn_mul_dig(t1, t0, 6);
bn_add(p, p, t1);
bn_mul(t1, t0, t0);
bn_mul_dig(t1, t1, 24);
bn_add(p, p, t1);
bn_mul(t1, t0, t0);
bn_mul(t1, t1, t0);
bn_mul_dig(t1, t1, 36);
bn_add(p, p, t1);
bn_mul(t0, t0, t0);
bn_mul(t1, t0, t0);
bn_mul_dig(t1, t1, 36);
bn_add(p, p, t1);
fp_prime_set_dense(p);
break;
#elif FP_PRIME == 160
case SECG_160:
/* p = 2^160 - 2^31 + 1. */
f[0] = -1;
f[1] = -31;
f[2] = 160;
fp_prime_set_pmers(f, 3);
break;
case SECG_160D:
/* p = 2^160 - 2^32 - 2^14 - 2^12 - 2^9 - 2^8 - 2^7 - 2^3 - 2^2 - 1.*/
f[0] = -1;
f[1] = -2;
f[2] = -3;
f[3] = -7;
f[4] = -8;
f[5] = -9;
f[6] = -12;
f[7] = -14;
f[8] = -32;
f[9] = 160;
fp_prime_set_pmers(f, 10);
break;
#elif FP_PRIME == 192
case NIST_192:
/* p = 2^192 - 2^64 - 1. */
f[0] = -1;
f[1] = -64;
f[2] = 192;
fp_prime_set_pmers(f, 3);
break;
case SECG_192:
/* p = 2^192 - 2^32 - 2^12 - 2^8 - 2^7 - 2^6 - 2^3 - 1.*/
f[0] = -1;
f[1] = -3;
f[2] = -6;
f[3] = -7;
f[4] = -8;
f[5] = -12;
f[6] = -32;
f[7] = 192;
fp_prime_set_pmers(f, 8);
break;
#elif FP_PRIME == 224
case NIST_224:
/* p = 2^224 - 2^96 + 1. */
f[0] = 1;
f[1] = -96;
f[2] = 224;
fp_prime_set_pmers(f, 3);
break;
case SECG_224:
/* p = 2^224 - 2^32 - 2^12 - 2^11 - 2^9 - 2^7 - 2^4 - 2 - 1.*/
f[0] = -1;
f[1] = -1;
f[2] = -4;
f[3] = -7;
f[4] = -9;
f[5] = -11;
f[6] = -12;
f[7] = -32;
f[8] = 224;
fp_prime_set_pmers(f, 9);
break;
#elif FP_PRIME == 254
case BN_254:
/* x = -4080000000000001. */
fp_param_get_var(t0);
/* p = 36 * x^4 + 36 * x^3 + 24 * x^2 + 6 * x + 1. */
bn_set_dig(p, 1);
bn_mul_dig(t1, t0, 6);
bn_add(p, p, t1);
bn_mul(t1, t0, t0);
bn_mul_dig(t1, t1, 24);
bn_add(p, p, t1);
bn_mul(t1, t0, t0);
bn_mul(t1, t1, t0);
bn_mul_dig(t1, t1, 36);
bn_add(p, p, t1);
bn_mul(t0, t0, t0);
bn_mul(t1, t0, t0);
bn_mul_dig(t1, t1, 36);
bn_add(p, p, t1);
fp_prime_set_dense(p);
break;
#elif FP_PRIME == 256
case NIST_256:
/* p = 2^256 - 2^224 + 2^192 + 2^96 - 1. */
f[0] = -1;
f[1] = 96;
f[2] = 192;
f[3] = -224;
f[4] = 256;
fp_prime_set_pmers(f, 5);
break;
case SECG_256:
/* p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1. */
f[0] = -1;
f[1] = -4;
f[2] = -6;
f[3] = -7;
f[4] = -8;
f[5] = -9;
f[6] = -32;
f[7] = 256;
fp_prime_set_pmers(f, 8);
break;
case BN_256:
/* x = 6000000000001F2D. */
fp_param_get_var(t0);
/* p = 36 * x^4 + 36 * x^3 + 24 * x^2 + 6 * x + 1. */
bn_set_dig(p, 1);
bn_mul_dig(t1, t0, 6);
bn_add(p, p, t1);
bn_mul(t1, t0, t0);
bn_mul_dig(t1, t1, 24);
bn_add(p, p, t1);
bn_mul(t1, t0, t0);
bn_mul(t1, t1, t0);
bn_mul_dig(t1, t1, 36);
bn_add(p, p, t1);
bn_mul(t0, t0, t0);
bn_mul(t1, t0, t0);
bn_mul_dig(t1, t1, 36);
bn_add(p, p, t1);
fp_prime_set_dense(p);
break;
#elif FP_PRIME == 384
case NIST_384:
/* p = 2^384 - 2^128 - 2^96 + 2^32 - 1. */
f[0] = -1;
f[1] = 32;
f[2] = -96;
f[3] = -128;
f[4] = 384;
fp_prime_set_pmers(f, 5);
break;
#elif FP_PRIME == 477
case B24_477:
fp_param_get_var(t0);
/* p = (u - 1)^2 * (u^8 - u^4 + 1) div 3 + u. */
bn_sub_dig(p, t0, 1);
bn_sqr(p, p);
bn_sqr(t1, t0);
bn_sqr(t1, t1);
bn_sqr(t2, t1);
bn_sub(t2, t2, t1);
bn_add_dig(t2, t2, 1);
bn_mul(p, p, t2);
bn_div_dig(p, p, 3);
bn_add(p, p, t0);
fp_prime_set_dense(p);
break;
#elif FP_PRIME == 508
case KSS_508:
fp_param_get_var(t0);
/* h = (49*u^2 + 245 * u + 343)/3 */
bn_mul_dig(p, t0, 245);
bn_add_dig(p, p, 200);
bn_add_dig(p, p, 143);
bn_sqr(t1, t0);
bn_mul_dig(t2, t1, 49);
bn_add(p, p, t2);
bn_div_dig(p, p, 3);
/* n = (u^6 + 37 * u^3 + 343)/343. */
bn_mul(t1, t1, t0);
bn_mul_dig(t2, t1, 37);
bn_sqr(t1, t1);
bn_add(t2, t2, t1);
bn_add_dig(t2, t2, 200);
bn_add_dig(t2, t2, 143);
bn_div_dig(t2, t2, 49);
bn_div_dig(t2, t2, 7);
bn_mul(p, p, t2);
/* t = (u^4 + 16 * u + 7)/7. */
bn_mul_dig(t1, t0, 16);
bn_add_dig(t1, t1, 7);
bn_sqr(t2, t0);
bn_sqr(t2, t2);
bn_add(t2, t2, t1);
bn_div_dig(t2, t2, 7);
bn_add(p, p, t2);
bn_sub_dig(p, p, 1);
fp_prime_set_dense(p);
break;
#elif FP_PRIME == 521
case NIST_521:
/* p = 2^521 - 1. */
f[0] = -1;
f[1] = 521;
fp_prime_set_pmers(f, 2);
break;
#elif FP_PRIME == 638
case BN_638:
fp_param_get_var(t0);
/* p = 36 * x^4 + 36 * x^3 + 24 * x^2 + 6 * x + 1. */
bn_set_dig(p, 1);
bn_mul_dig(t1, t0, 6);
bn_add(p, p, t1);
bn_mul(t1, t0, t0);
bn_mul_dig(t1, t1, 24);
bn_add(p, p, t1);
bn_mul(t1, t0, t0);
bn_mul(t1, t1, t0);
bn_mul_dig(t1, t1, 36);
bn_add(p, p, t1);
bn_mul(t0, t0, t0);
bn_mul(t1, t0, t0);
bn_mul_dig(t1, t1, 36);
bn_add(p, p, t1);
fp_prime_set_dense(p);
break;
case B12_638:
fp_param_get_var(t0);
/* p = (x^2 - 2x + 1) * (x^4 - x^2 + 1)/3 + x. */
bn_sqr(t1, t0);
bn_sqr(p, t1);
bn_sub(p, p, t1);
bn_add_dig(p, p, 1);
bn_sub(t1, t1, t0);
bn_sub(t1, t1, t0);
bn_add_dig(t1, t1, 1);
bn_mul(p, p, t1);
bn_div_dig(p, p, 3);
bn_add(p, p, t0);
fp_prime_set_dense(p);
break;
#elif FP_PRIME == 1536
case SS_1536:
fp_param_get_var(t0);
bn_read_str(p, SS_P1536, strlen(SS_P1536), 16);
bn_mul(p, p, t0);
bn_dbl(p, p);
bn_sub_dig(p, p, 1);
fp_prime_set_dense(p);
break;
#else
default:
bn_gen_prime(p, FP_BITS);
fp_prime_set_dense(p);
core_get()->fp_id = 0;
break;
#endif
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(t0);
bn_free(t1);
bn_free(t2);
bn_free(p);
}
}
