int igraph_biguint_mul(igraph_biguint_t *res, igraph_biguint_t *left,
igraph_biguint_t *right) {
long int size_left=igraph_biguint_size(left);
long int size_right=igraph_biguint_size(right);
if (size_left > size_right) {
IGRAPH_CHECK(igraph_biguint_resize(right, size_left));
size_right=size_left;
} else if (size_left < size_right) {
IGRAPH_CHECK(igraph_biguint_resize(left, size_right));
size_left=size_right;
}
IGRAPH_CHECK(igraph_biguint_resize(res, 2*size_left));
bn_mul( VECTOR(res->v), VECTOR(left->v), VECTOR(right->v), size_left );
return 0;
}
// int appears on rhs
status_t element_div_int(element_t c, element_t a, integer_t b)
{
GroupType type = a->type;
EXIT_IF_NOT_SAME(c, a);
LEAVE_IF( c->isInitialized != TRUE || a->isInitialized != TRUE, "uninitialized arguments.");
LEAVE_IF( c->type != type, "result initialized but invalid type.");
if(type == ZR) {
if(bn_is_zero(b)) return ELEMENT_DIV_ZERO;
// if(bn_is_one(a->bn)) {
// element_set_int(a, b);
// return element_invert(c, a); // not going to work
// }
integer_t s;
bn_inits(s);
// compute c = (1 / b) mod order
bn_gcd_ext(s, c->bn, NULL, b, a->order);
if(bn_sign(c->bn) == BN_NEG) bn_add(c->bn, c->bn, a->order);
if(bn_is_one(a->bn) && bn_sign(a->bn) == BN_POS) {
bn_free(s);
return ELEMENT_OK;
}
// remainder of ((a * c) / order)
// c = (a * c) / order (remainder only)
bn_mul(s, a->bn, c->bn);
bn_div_rem(s, c->bn, s, a->order);
// if(bn_sign(c->bn) == BN_NEG) bn_add(c->bn, c->bn, a->order);
bn_free(s);
// bn_div(c->bn, a->bn, b);
// bn_mod(c->bn, c->bn, c->order);
}
else if(type == G1 || type == G2 || type == GT) {
if(bn_is_one(b)) {
return element_set(c, a);
}
// TODO: other cases: b > 1 (ZR)?
}
else {
return ELEMENT_INVALID_TYPES;
}
return ELEMENT_OK;
}
int cp_bdpe_enc(uint8_t *out, int *out_len, dig_t in, bdpe_t pub) {
bn_t m, u;
int size, result = STS_OK;
bn_null(m);
bn_null(u);
size = bn_size_bin(pub->n);
if (in > pub->t) {
return STS_ERR;
}
TRY {
bn_new(m);
bn_new(u);
bn_set_dig(m, in);
bn_rand_mod(u, pub->n);
bn_mxp(m, pub->y, m, pub->n);
bn_mxp_dig(u, u, pub->t, pub->n);
bn_mul(m, m, u);
bn_mod(m, m, pub->n);
if (size <= *out_len) {
*out_len = size;
memset(out, 0, *out_len);
bn_write_bin(out, size, m);
} else {
result = STS_ERR;
}
}
CATCH_ANY {
result = STS_ERR;
}
FINALLY {
bn_free(m);
bn_free(u);
}
return result;
}
void ep2_curve_get_vs(bn_t *v) {
bn_t x, t;
bn_null(x);
bn_null(t);
TRY {
bn_new(x);
bn_new(t);
fp_param_get_var(x);
bn_mul_dig(v[0], x, 3);
bn_add_dig(v[0], v[0], 1);
bn_copy(v[1], x);
bn_copy(v[2], x);
bn_copy(v[3], x);
bn_sqr(x, x);
bn_lsh(t, x, 1);
bn_add(v[0], v[0], t);
bn_add(v[3], v[3], t);
bn_lsh(t, t, 1);
bn_add(v[2], v[2], t);
bn_lsh(t, t, 1);
bn_add(v[1], v[1], t);
fp_param_get_var(t);
bn_mul(x, x, t);
bn_mul_dig(t, x, 6);
bn_add(v[2], v[2], t);
bn_lsh(t, t, 1);
bn_add(v[1], v[1], t);
bn_neg(v[3], v[3]);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
bn_free(x);
bn_free(t);
}
}
int cp_psb_sig(g1_t a, g1_t b, uint8_t *msgs[], int lens[], bn_t r, bn_t s[],
int l) {
bn_t m, n, t;
int i, result = RLC_OK;
bn_null(m);
bn_null(n);
bn_null(t);
TRY {
bn_new(m);
bn_new(n);
bn_new(t);
/* Choose random a in G1. */
g1_rand(a);
/* Compute b = a^x+\sum y_im_i. */
g1_get_ord(n);
bn_copy(t, r);
for (i = 0; i < l; i++) {
bn_read_bin(m, msgs[i], lens[i]);
bn_mod(m, m, n);
bn_mul(m, m, s[i]);
bn_mod(m, m, n);
bn_add(t, t, m);
bn_mod(t, t, n);
}
g1_mul(b, a, t);
}
CATCH_ANY {
result = RLC_ERR;
}
FINALLY {
bn_free(m);
bn_free(n);
bn_free(t);
}
return result;
}
void bn_mxp_slide(bn_t c, const bn_t a, const bn_t b, const bn_t m) {
bn_t tab[TABLE_SIZE], t, u, r;
int i, j, l, w = 1;
uint8_t win[BN_BITS];
bn_null(t);
bn_null(u);
bn_null(r);
/* Initialize table. */
for (i = 0; i < TABLE_SIZE; i++) {
bn_null(tab[i]);
}
TRY {
/* Find window size. */
i = bn_bits(b);
if (i <= 21) {
w = 2;
} else if (i <= 32) {
w = 3;
} else if (i <= 128) {
w = 4;
} else if (i <= 256) {
w = 5;
} else {
w = 6;
}
for (i = 1; i < (1 << w); i += 2) {
bn_new(tab[i]);
}
bn_new(t);
bn_new(u);
bn_new(r);
bn_mod_pre(u, m);
#if BN_MOD == MONTY
bn_set_dig(r, 1);
bn_mod_monty_conv(r, r, m);
bn_mod_monty_conv(t, a, m);
#else /* BN_MOD == BARRT || BN_MOD == RADIX */
bn_set_dig(r, 1);
bn_copy(t, a);
#endif
bn_copy(tab[1], t);
bn_sqr(t, tab[1]);
bn_mod(t, t, m, u);
/* Create table. */
for (i = 1; i < 1 << (w - 1); i++) {
bn_mul(tab[2 * i + 1], tab[2 * i - 1], t);
bn_mod(tab[2 * i + 1], tab[2 * i + 1], m, u);
}
l = BN_BITS + 1;
bn_rec_slw(win, &l, b, w);
for (i = 0; i < l; i++) {
if (win[i] == 0) {
bn_sqr(r, r);
bn_mod(r, r, m, u);
} else {
for (j = 0; j < util_bits_dig(win[i]); j++) {
bn_sqr(r, r);
bn_mod(r, r, m, u);
}
bn_mul(r, r, tab[win[i]]);
bn_mod(r, r, m, u);
}
}
bn_trim(r);
#if BN_MOD == MONTY
bn_mod_monty_back(c, r, m);
#else
bn_copy(c, r);
#endif
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
for (i = 1; i < (1 << w); i++) {
bn_free(tab[i]);
}
bn_free(u);
bn_free(t);
bn_free(r);
}
}
int cp_rsa_enc(uint8_t *out, int *out_len, uint8_t *in, int in_len, rsa_t pub) {
bn_t m, eb;
int size, pad_len, result = STS_OK;
bn_null(m);
bn_null(eb);
size = bn_size_bin(pub->n);
if (pub == NULL || in_len <= 0 || in_len > (size - RSA_PAD_LEN)) {
return STS_ERR;
}
TRY {
bn_new(m);
bn_new(eb);
bn_zero(m);
bn_zero(eb);
#if CP_RSAPD == BASIC
if (pad_basic(eb, &pad_len, in_len, size, RSA_ENC) == STS_OK) {
#elif CP_RSAPD == PKCS1
if (pad_pkcs1(eb, &pad_len, in_len, size, RSA_ENC) == STS_OK) {
#elif CP_RSAPD == PKCS2
if (pad_pkcs2(eb, &pad_len, in_len, size, RSA_ENC) == STS_OK) {
#endif
bn_read_bin(m, in, in_len);
bn_add(eb, eb, m);
#if CP_RSAPD == PKCS2
pad_pkcs2(eb, &pad_len, in_len, size, RSA_ENC_FIN);
#endif
bn_mxp(eb, eb, pub->e, pub->n);
if (size <= *out_len) {
*out_len = size;
memset(out, 0, *out_len);
bn_write_bin(out, size, eb);
} else {
result = STS_ERR;
}
} else {
result = STS_ERR;
}
}
CATCH_ANY {
result = STS_ERR;
}
FINALLY {
bn_free(m);
bn_free(eb);
}
return result;
}
#if CP_RSA == BASIC || !defined(STRIP)
int cp_rsa_dec_basic(uint8_t *out, int *out_len, uint8_t *in, int in_len, rsa_t prv) {
bn_t m, eb;
int size, pad_len, result = STS_OK;
size = bn_size_bin(prv->n);
if (prv == NULL || in_len != size || in_len < RSA_PAD_LEN) {
return STS_ERR;
}
bn_null(m);
bn_null(eb);
TRY {
bn_new(m);
bn_new(eb);
bn_read_bin(eb, in, in_len);
bn_mxp(eb, eb, prv->d, prv->n);
if (bn_cmp(eb, prv->n) != CMP_LT) {
result = STS_ERR;
}
#if CP_RSAPD == BASIC
if (pad_basic(eb, &pad_len, in_len, size, RSA_DEC) == STS_OK) {
#elif CP_RSAPD == PKCS1
if (pad_pkcs1(eb, &pad_len, in_len, size, RSA_DEC) == STS_OK) {
#elif CP_RSAPD == PKCS2
if (pad_pkcs2(eb, &pad_len, in_len, size, RSA_DEC) == STS_OK) {
#endif
size = size - pad_len;
if (size <= *out_len) {
memset(out, 0, size);
bn_write_bin(out, size, eb);
*out_len = size;
} else {
result = STS_ERR;
}
} else {
result = STS_ERR;
}
}
CATCH_ANY {
result = STS_ERR;
}
FINALLY {
bn_free(m);
bn_free(eb);
}
return result;
}
#endif
#if CP_RSA == QUICK || !defined(STRIP)
int cp_rsa_dec_quick(uint8_t *out, int *out_len, uint8_t *in, int in_len, rsa_t prv) {
bn_t m, eb;
int size, pad_len, result = STS_OK;
bn_null(m);
bn_null(eb);
size = bn_size_bin(prv->n);
if (prv == NULL || in_len != size || in_len < RSA_PAD_LEN) {
return STS_ERR;
}
TRY {
bn_new(m);
bn_new(eb);
bn_read_bin(eb, in, in_len);
bn_copy(m, eb);
/* m1 = c^dP mod p. */
bn_mxp(eb, eb, prv->dp, prv->p);
/* m2 = c^dQ mod q. */
bn_mxp(m, m, prv->dq, prv->q);
/* m1 = m1 - m2 mod p. */
bn_sub(eb, eb, m);
while (bn_sign(eb) == BN_NEG) {
bn_add(eb, eb, prv->p);
}
bn_mod(eb, eb, prv->p);
/* m1 = qInv(m1 - m2) mod p. */
bn_mul(eb, eb, prv->qi);
bn_mod(eb, eb, prv->p);
/* m = m2 + m1 * q. */
bn_mul(eb, eb, prv->q);
bn_add(eb, eb, m);
if (bn_cmp(eb, prv->n) != CMP_LT) {
result = STS_ERR;
}
#if CP_RSAPD == BASIC
if (pad_basic(eb, &pad_len, in_len, size, RSA_DEC) == STS_OK) {
#elif CP_RSAPD == PKCS1
if (pad_pkcs1(eb, &pad_len, in_len, size, RSA_DEC) == STS_OK) {
#elif CP_RSAPD == PKCS2
if (pad_pkcs2(eb, &pad_len, in_len, size, RSA_DEC) == STS_OK) {
#endif
size = size - pad_len;
if (size <= *out_len) {
memset(out, 0, size);
bn_write_bin(out, size, eb);
*out_len = size;
} else {
result = STS_ERR;
}
} else {
result = STS_ERR;
}
}
CATCH_ANY {
result = STS_ERR;
}
FINALLY {
bn_free(m);
bn_free(eb);
}
return result;
}
#endif
#if CP_RSA == BASIC || !defined(STRIP)
int cp_rsa_sig_basic(uint8_t *sig, int *sig_len, uint8_t *msg, int msg_len, int hash, rsa_t prv) {
bn_t m, eb;
int size, pad_len, result = STS_OK;
uint8_t h[MD_LEN];
if (prv == NULL || msg_len < 0) {
return STS_ERR;
}
pad_len = (!hash ? MD_LEN : msg_len);
#if CP_RSAPD == PKCS2
size = bn_bits(prv->n) - 1;
size = (size / 8) + (size % 8 > 0);
if (pad_len > (size - 2)) {
return STS_ERR;
}
#else
size = bn_size_bin(prv->n);
if (pad_len > (size - RSA_PAD_LEN)) {
return STS_ERR;
}
#endif
bn_null(m);
bn_null(eb);
TRY {
bn_new(m);
bn_new(eb);
bn_zero(m);
bn_zero(eb);
int operation = (!hash ? RSA_SIG : RSA_SIG_HASH);
#if CP_RSAPD == BASIC
if (pad_basic(eb, &pad_len, pad_len, size, operation) == STS_OK) {
#elif CP_RSAPD == PKCS1
if (pad_pkcs1(eb, &pad_len, pad_len, size, operation) == STS_OK) {
#elif CP_RSAPD == PKCS2
if (pad_pkcs2(eb, &pad_len, pad_len, size, operation) == STS_OK) {
#endif
if (!hash) {
md_map(h, msg, msg_len);
bn_read_bin(m, h, MD_LEN);
bn_add(eb, eb, m);
} else {
bn_read_bin(m, msg, msg_len);
bn_add(eb, eb, m);
}
#if CP_RSAPD == PKCS2
pad_pkcs2(eb, &pad_len, bn_bits(prv->n), size, RSA_SIG_FIN);
#endif
bn_mxp(eb, eb, prv->d, prv->n);
size = bn_size_bin(prv->n);
if (size <= *sig_len) {
memset(sig, 0, size);
bn_write_bin(sig, size, eb);
*sig_len = size;
} else {
result = STS_ERR;
}
} else {
result = STS_ERR;
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(m);
bn_free(eb);
}
return result;
}
#endif
#if CP_RSA == QUICK || !defined(STRIP)
int cp_rsa_sig_quick(uint8_t *sig, int *sig_len, uint8_t *msg, int msg_len, int hash, rsa_t prv) {
bn_t m, eb;
int pad_len, size, result = STS_OK;
uint8_t h[MD_LEN];
if (prv == NULL || msg_len < 0) {
return STS_ERR;
}
pad_len = (!hash ? MD_LEN : msg_len);
#if CP_RSAPD == PKCS2
size = bn_bits(prv->n) - 1;
size = (size / 8) + (size % 8 > 0);
if (pad_len > (size - 2)) {
return STS_ERR;
}
#else
size = bn_size_bin(prv->n);
if (pad_len > (size - RSA_PAD_LEN)) {
return STS_ERR;
}
#endif
bn_null(m);
bn_null(eb);
TRY {
bn_new(m);
bn_new(eb);
bn_zero(m);
bn_zero(eb);
int operation = (!hash ? RSA_SIG : RSA_SIG_HASH);
#if CP_RSAPD == BASIC
if (pad_basic(eb, &pad_len, pad_len, size, operation) == STS_OK) {
#elif CP_RSAPD == PKCS1
if (pad_pkcs1(eb, &pad_len, pad_len, size, operation) == STS_OK) {
#elif CP_RSAPD == PKCS2
if (pad_pkcs2(eb, &pad_len, pad_len, size, operation) == STS_OK) {
#endif
if (!hash) {
md_map(h, msg, msg_len);
bn_read_bin(m, h, MD_LEN);
bn_add(eb, eb, m);
} else {
bn_read_bin(m, msg, msg_len);
bn_add(eb, eb, m);
}
#if CP_RSAPD == PKCS2
pad_pkcs2(eb, &pad_len, bn_bits(prv->n), size, RSA_SIG_FIN);
#endif
bn_copy(m, eb);
/* m1 = c^dP mod p. */
bn_mxp(eb, eb, prv->dp, prv->p);
/* m2 = c^dQ mod q. */
bn_mxp(m, m, prv->dq, prv->q);
/* m1 = m1 - m2 mod p. */
bn_sub(eb, eb, m);
while (bn_sign(eb) == BN_NEG) {
bn_add(eb, eb, prv->p);
}
bn_mod(eb, eb, prv->p);
/* m1 = qInv(m1 - m2) mod p. */
bn_mul(eb, eb, prv->qi);
bn_mod(eb, eb, prv->p);
/* m = m2 + m1 * q. */
bn_mul(eb, eb, prv->q);
bn_add(eb, eb, m);
bn_mod(eb, eb, prv->n);
size = bn_size_bin(prv->n);
if (size <= *sig_len) {
memset(sig, 0, size);
bn_write_bin(sig, size, eb);
*sig_len = size;
} else {
result = STS_ERR;
}
} else {
result = STS_ERR;
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(m);
bn_free(eb);
}
return result;
}
#endif
int cp_rsa_ver(uint8_t *sig, int sig_len, uint8_t *msg, int msg_len, int hash, rsa_t pub) {
bn_t m, eb;
int size, pad_len, result;
uint8_t h1[MAX(msg_len, MD_LEN) + 8], h2[MAX(msg_len, MD_LEN)];
/* We suppose that the signature is invalid. */
result = 0;
if (pub == NULL || msg_len < 0) {
return 0;
}
pad_len = (!hash ? MD_LEN : msg_len);
#if CP_RSAPD == PKCS2
size = bn_bits(pub->n) - 1;
if (size % 8 == 0) {
size = size / 8 - 1;
} else {
size = bn_size_bin(pub->n);
}
if (pad_len > (size - 2)) {
return 0;
}
#else
size = bn_size_bin(pub->n);
if (pad_len > (size - RSA_PAD_LEN)) {
return 0;
}
#endif
bn_null(m);
bn_null(eb);
TRY {
bn_new(m);
bn_new(eb);
bn_read_bin(eb, sig, sig_len);
bn_mxp(eb, eb, pub->e, pub->n);
int operation = (!hash ? RSA_VER : RSA_VER_HASH);
#if CP_RSAPD == BASIC
if (pad_basic(eb, &pad_len, MD_LEN, size, operation) == STS_OK) {
#elif CP_RSAPD == PKCS1
if (pad_pkcs1(eb, &pad_len, MD_LEN, size, operation) == STS_OK) {
#elif CP_RSAPD == PKCS2
if (pad_pkcs2(eb, &pad_len, bn_bits(pub->n), size, operation) == STS_OK) {
#endif
#if CP_RSAPD == PKCS2
memset(h1, 0, 8);
if (!hash) {
md_map(h1 + 8, msg, msg_len);
md_map(h2, h1, MD_LEN + 8);
memset(h1, 0, MD_LEN);
bn_write_bin(h1, size - pad_len, eb);
/* Everything went ok, so signature status is changed. */
result = util_cmp_const(h1, h2, MD_LEN);
} else {
memcpy(h1 + 8, msg, msg_len);
md_map(h2, h1, MD_LEN + 8);
memset(h1, 0, msg_len);
bn_write_bin(h1, size - pad_len, eb);
/* Everything went ok, so signature status is changed. */
result = util_cmp_const(h1, h2, msg_len);
}
#else
memset(h1, 0, MAX(msg_len, MD_LEN));
bn_write_bin(h1, size - pad_len, eb);
if (!hash) {
md_map(h2, msg, msg_len);
/* Everything went ok, so signature status is changed. */
result = util_cmp_const(h1, h2, MD_LEN);
} else {
/* Everything went ok, so signature status is changed. */
result = util_cmp_const(h1, msg, msg_len);
}
#endif
result = (result == CMP_EQ ? 1 : 0);
} else {
result = 0;
}
}
CATCH_ANY {
result = 0;
}
FINALLY {
bn_free(m);
bn_free(eb);
}
return result;
}
int cp_rsa_gen_quick(rsa_t pub, rsa_t prv, int bits) {
bn_t t, r;
int result = STS_OK;
if (pub == NULL || prv == NULL || bits == 0) {
return STS_ERR;
}
bn_null(t);
bn_null(r);
TRY {
bn_new(t);
bn_new(r);
/* Generate different primes p and q. */
do {
bn_gen_prime(prv->p, bits / 2);
bn_gen_prime(prv->q, bits / 2);
} while (bn_cmp(prv->p, prv->q) == CMP_EQ);
/* Swap p and q so that p is smaller. */
if (bn_cmp(prv->p, prv->q) == CMP_LT) {
bn_copy(t, prv->p);
bn_copy(prv->p, prv->q);
bn_copy(prv->q, t);
}
/* n = pq. */
bn_mul(pub->n, prv->p, prv->q);
bn_copy(prv->n, pub->n);
bn_sub_dig(prv->p, prv->p, 1);
bn_sub_dig(prv->q, prv->q, 1);
/* phi(n) = (p - 1)(q - 1). */
bn_mul(t, prv->p, prv->q);
bn_set_2b(pub->e, 16);
bn_add_dig(pub->e, pub->e, 1);
/* d = e^(-1) mod phi(n). */
bn_gcd_ext(r, prv->d, NULL, pub->e, t);
if (bn_sign(prv->d) == BN_NEG) {
bn_add(prv->d, prv->d, t);
}
if (bn_cmp_dig(r, 1) == CMP_EQ) {
/* dP = d mod (p - 1). */
bn_mod(prv->dp, prv->d, prv->p);
/* dQ = d mod (q - 1). */
bn_mod(prv->dq, prv->d, prv->q);
bn_add_dig(prv->p, prv->p, 1);
bn_add_dig(prv->q, prv->q, 1);
/* qInv = q^(-1) mod p. */
bn_gcd_ext(r, prv->qi, NULL, prv->q, prv->p);
if (bn_sign(prv->qi) == BN_NEG) {
bn_add(prv->qi, prv->qi, prv->p);
}
result = STS_OK;
}
}
CATCH_ANY {
result = STS_ERR;
}
FINALLY {
bn_free(t);
bn_free(r);
}
return result;
}
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;
}
void bn_gen_prime_stron(bn_t a, int bits) {
dig_t i, j;
int found, k;
bn_t r, s, t;
bn_null(r);
bn_null(s);
bn_null(t);
TRY {
bn_new(r);
bn_new(s);
bn_new(t);
do {
do {
/* Generate two large primes r and s. */
bn_rand(s, BN_POS, bits / 2 - BN_DIGIT / 2);
bn_rand(t, BN_POS, bits / 2 - BN_DIGIT / 2);
} while (!bn_is_prime(s) || !bn_is_prime(t));
found = 1;
bn_rand(a, BN_POS, bits / 2 - bn_bits(t) - 1);
i = a->dp[0];
bn_dbl(t, t);
do {
/* Find first prime r = 2 * i * t + 1. */
bn_mul_dig(r, t, i);
bn_add_dig(r, r, 1);
i++;
if (bn_bits(r) > bits / 2 - 1) {
found = 0;
break;
}
} while (!bn_is_prime(r));
if (found == 0) {
continue;
}
/* Compute t = 2 * (s^(r-2) mod r) * s - 1. */
bn_sub_dig(t, r, 2);
#if BN_MOD != PMERS
bn_mxp(t, s, t, r);
#else
bn_exp(t, s, t, r);
#endif
bn_mul(t, t, s);
bn_dbl(t, t);
bn_sub_dig(t, t, 1);
k = bits - bn_bits(r);
k -= bn_bits(s);
bn_rand(a, BN_POS, k);
j = a->dp[0];
do {
/* Find first prime a = t + 2 * j * r * s. */
bn_mul(a, r, s);
bn_mul_dig(a, a, j);
bn_dbl(a, a);
bn_add(a, a, t);
j++;
if (bn_bits(a) > bits) {
found = 0;
break;
}
} while (!bn_is_prime(a));
} while (found == 0 && bn_bits(a) != bits);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(r);
bn_free(s);
bn_free(t);
}
}
void cp_ecss_sig(bn_t e, bn_t s, unsigned char *msg, int len, bn_t d) {
bn_t n, k, x, r;
ec_t p;
unsigned char hash[MD_LEN];
unsigned char m[len + EC_BYTES];
bn_null(n);
bn_null(k);
bn_null(x);
bn_null(r);
ec_null(p);
TRY {
bn_new(n);
bn_new(k);
bn_new(x);
bn_new(r);
ec_new(p);
ec_curve_get_ord(n);
do {
do {
bn_rand(k, BN_POS, bn_bits(n));
bn_mod(k, k, n);
} while (bn_is_zero(k));
ec_mul_gen(p, k);
ec_get_x(x, p);
bn_mod(r, x, n);
} while (bn_is_zero(r));
memcpy(m, msg, len);
bn_write_bin(m + len, EC_BYTES, r);
md_map(hash, m, len + EC_BYTES);
if (8 * MD_LEN > bn_bits(n)) {
len = CEIL(bn_bits(n), 8);
bn_read_bin(e, hash, len);
bn_rsh(e, e, 8 * MD_LEN - bn_bits(n));
} else {
bn_read_bin(e, hash, MD_LEN);
}
bn_mod(e, e, n);
bn_mul(s, d, e);
bn_mod(s, s, n);
bn_sub(s, n, s);
bn_add(s, s, k);
bn_mod(s, s, n);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(n);
bn_free(k);
bn_free(x);
bn_free(r);
ec_free(p);
}
}
int cp_bgn_dec(dig_t *out, gt_t in[4], bgn_t prv) {
int i, result = STS_ERR;
g1_t g;
g2_t h;
gt_t t[4];
bn_t n, r, s;
bn_null(n);
bn_null(r);
bn_null(s);
g1_null(g);
g2_null(h);
TRY {
bn_new(n);
bn_new(r);
bn_new(s);
g1_new(g);
g2_new(h);
for (i = 0; i < 4; i++) {
gt_null(t[i]);
gt_new(t[i]);
}
gt_exp(t[0], in[0], prv->x);
gt_exp(t[0], t[0], prv->x);
gt_mul(t[1], in[1], in[2]);
gt_exp(t[1], t[1], prv->x);
gt_inv(t[1], t[1]);
gt_mul(t[3], in[3], t[1]);
gt_mul(t[3], t[3], t[0]);
gt_get_ord(n);
g1_get_gen(g);
g2_get_gen(h);
bn_mul(r, prv->x, prv->y);
bn_sqr(r, r);
bn_mul(s, prv->x, prv->y);
bn_mul(s, s, prv->z);
bn_sub(r, r, s);
bn_sub(r, r, s);
bn_sqr(s, prv->z);
bn_add(r, r, s);
bn_mod(r, r, n);
pc_map(t[1], g, h);
gt_exp(t[1], t[1], r);
gt_copy(t[2], t[1]);
if (gt_is_unity(t[3]) == 1) {
*out = 0;
result = STS_OK;
} else {
for (i = 0; i < INT_MAX; i++) {
if (gt_cmp(t[2], t[3]) == CMP_EQ) {
*out = i + 1;
result = STS_OK;
break;
}
gt_mul(t[2], t[2], t[1]);
}
}
} CATCH_ANY {
result = STS_ERR;
} FINALLY {
bn_free(n);
bn_free(r);
bn_free(s);
g1_free(g);
g2_free(h);
for (i = 0; i < 4; i++) {
gt_free(t[i]);
}
}
return result;
}
int cp_ecss_sig(bn_t e, bn_t s, uint8_t *msg, int len, bn_t d) {
bn_t n, k, x, r;
ec_t p;
uint8_t hash[MD_LEN];
uint8_t m[len + FC_BYTES];
int result = STS_OK;
bn_null(n);
bn_null(k);
bn_null(x);
bn_null(r);
ec_null(p);
TRY {
bn_new(n);
bn_new(k);
bn_new(x);
bn_new(r);
ec_new(p);
ec_curve_get_ord(n);
do {
do {
bn_rand(k, BN_POS, bn_bits(n));
bn_mod(k, k, n);
} while (bn_is_zero(k));
ec_mul_gen(p, k);
ec_get_x(x, p);
bn_mod(r, x, n);
} while (bn_is_zero(r));
memcpy(m, msg, len);
bn_write_bin(m + len, FC_BYTES, r);
md_map(hash, m, len + FC_BYTES);
if (8 * MD_LEN > bn_bits(n)) {
len = CEIL(bn_bits(n), 8);
bn_read_bin(e, hash, len);
bn_rsh(e, e, 8 * MD_LEN - bn_bits(n));
} else {
bn_read_bin(e, hash, MD_LEN);
}
bn_mod(e, e, n);
bn_mul(s, d, e);
bn_mod(s, s, n);
bn_sub(s, n, s);
bn_add(s, s, k);
bn_mod(s, s, n);
}
CATCH_ANY {
result = STS_ERR;
}
FINALLY {
bn_free(n);
bn_free(k);
bn_free(x);
bn_free(r);
ec_free(p);
}
return result;
}
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);
}
}
