void fp_invn_low(dig_t *c, const dig_t *a) { mp_size_t cn; align dig_t s[FP_DIGS], t[2 * FP_DIGS], u[FP_DIGS + 1]; #if FP_RDC == MONTY dv_zero(t + FP_DIGS, FP_DIGS); dv_copy(t, a, FP_DIGS); fp_rdcn_low(u, t); #else fp_copy(u, a); #endif dv_copy(s, fp_prime_get(), FP_DIGS); mpn_gcdext(t, c, &cn, u, FP_DIGS, s, FP_DIGS); if (cn < 0) { dv_zero(c - cn, FP_DIGS + cn); mpn_sub_n(c, fp_prime_get(), c, FP_DIGS); } else { dv_zero(c + cn, FP_DIGS - cn); } #if FP_RDC == MONTY dv_zero(t, FP_DIGS); dv_copy(t + FP_DIGS, c, FP_DIGS); mpn_tdiv_qr(u, c, 0, t, 2 * FP_DIGS, fp_prime_get(), FP_DIGS); #endif }
/** * Multiplies two binary field elements using shift-and-add multiplication. * * @param c - the result. * @param a - the first binary field element. * @param b - the second binary field element. * @param size - the number of digits to multiply. */ static void fb_mul_basic_imp(dig_t *c, const dig_t *a, const dig_t *b, int size) { int i; dv_t s; dv_null(s); TRY { /* We need a temporary variable so that c can be a or b. */ dv_new(s); dv_zero(s, 2 * FB_DIGS); dv_copy(s, b, size); dv_zero(c, 2 * size); if (a[0] & 1) { dv_copy(c, b, size); } for (i = 1; i <= (FB_DIGIT * size) - 1; i++) { fb_lsh1_low(s, s); fb_rdc(s, s); if (fb_get_bit(a, i)) { fb_add(c, c, s); } } } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { dv_free(s); } }
void fp_rdc_basic(fp_t c, dv_t a) { dv_t t0, t1, t2, t3; dv_null(t0); dv_null(t1); dv_null(t2); dv_null(t3); TRY { dv_new(t0); dv_new(t1); dv_new(t2); dv_new(t3); dv_copy(t2, a, 2 * FP_DIGS); dv_copy(t3, fp_prime_get(), FP_DIGS); bn_divn_low(t0, t1, t2, 2 * FP_DIGS, t3, FP_DIGS); fp_copy(c, t1); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { dv_free(t0); dv_free(t1); dv_free(t2); dv_free(t3); } }
void fp12_mul_lazyr(fp12_t c, fp12_t a, fp12_t b) { dv6_t u0, u1, u2, u3; fp6_t t0, t1; dv6_null(u0); dv6_null(u1); dv6_null(u2); dv6_null(u3); fp6_null(t0); fp6_null(t0); fp6_null(t1); TRY { dv6_new(u0); dv6_new(u1); dv6_new(u2); dv6_new(u3); fp6_new(t0); fp6_new(t1); /* Karatsuba algorithm. */ /* u0 = a_0 * b_0. */ fp6_mul_unr(u0, a[0], b[0]); /* u1 = a_1 * b_1. */ fp6_mul_unr(u1, a[1], b[1]); /* t1 = a_0 + a_1. */ fp6_add(t0, a[0], a[1]); /* t0 = b_0 + b_1. */ fp6_add(t1, b[0], b[1]); /* u2 = (a_0 + a_1) * (b_0 + b_1) */ fp6_mul_unr(u2, t0, t1); /* c_1 = u2 - a_0b_0 - a_1b_1. */ for (int i = 0; i < 3; i++) { fp2_addc_low(u3[i], u0[i], u1[i]); fp2_subc_low(u2[i], u2[i], u3[i]); fp2_rdcn_low(c[1][i], u2[i]); } /* c_0 = a_0b_0 + v * a_1b_1. */ fp2_nord_low(u2[0], u1[2]); dv_copy(u2[1][0], u1[0][0], 2 * RLC_FP_DIGS); dv_copy(u2[1][1], u1[0][1], 2 * RLC_FP_DIGS); dv_copy(u2[2][0], u1[1][0], 2 * RLC_FP_DIGS); dv_copy(u2[2][1], u1[1][1], 2 * RLC_FP_DIGS); for (int i = 0; i < 3; i++) { fp2_addc_low(u2[i], u0[i], u2[i]); fp2_rdcn_low(c[0][i], u2[i]); } } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { dv6_free(u0); dv6_free(u1); dv6_free(u2); dv6_free(u3); fp6_free(t0); fp6_free(t1); } }
void fp2_nord_low(dv2_t c, dv2_t a) { dv2_t t; bn_t b; dv2_null(t); bn_null(b); TRY { dv2_new(t); bn_new(b); #ifdef FP_QNRES /* If p = 3 mod 8, (1 + i) is a QNR/CNR. */ /* (a_0 + a_1 * i) * (1 + i) = (a_0 - a_1) + (a_0 + a_1) * u. */ dv_copy(t[0], a[1], 2 * FP_DIGS); fp_addc_low(c[1], a[0], a[1]); fp_subc_low(c[0], a[0], t[0]); #else switch (fp_prime_get_mod8()) { case 3: /* If p = 3 mod 8, (1 + u) is a QNR, u^2 = -1. */ /* (a_0 + a_1 * u) * (1 + u) = (a_0 - a_1) + (a_0 + a_1) * u. */ dv_copy(t[0], a[1], 2 * FP_DIGS); fp_addc_low(c[1], a[0], a[1]); fp_subc_low(c[0], a[0], t[0]); break; case 1: case 5: /* If p = 1,5 mod 8, (u) is a QNR. */ dv_copy(t[0], a[0], 2 * FP_DIGS); dv_zero(t[1], FP_DIGS); dv_copy(t[1] + FP_DIGS, fp_prime_get(), FP_DIGS); fp_subc_low(c[0], t[1], a[1]); for (int i = -1; i > fp_prime_get_qnr(); i--) { fp_subc_low(c[0], c[0], a[1]); } dv_copy(c[1], t[0], 2 * FP_DIGS); break; case 7: /* If p = 7 mod 8, (2 + u) is a QNR/CNR. */ fp2_addc_low(t, a, a); fp_subc_low(c[0], t[0], a[1]); fp_addc_low(c[1], t[1], a[0]); break; default: THROW(ERR_NO_VALID); break; } #endif } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { dv2_free(t); bn_free(b); } }
void fp8_sqr_lazyr(fp8_t c, fp8_t a) { fp4_t t; dv4_t u0, u1, u2; fp4_null(t); dv4_null(u0); dv4_null(u1); dv4_null(u2); TRY { fp4_new(t); dv4_new(u0); dv4_new(u1); dv4_new(u2); /* t0 = a^2. */ fp4_sqr_unr(u0, a[0]); /* t1 = b^2. */ fp4_sqr_unr(u1, a[1]); fp4_add(t, a[0], a[1]); /* c = a^2 + b^2 * E. */ dv_copy(u2[1][0], u1[0][0], 2 * RLC_FP_DIGS); dv_copy(u2[1][1], u1[0][1], 2 * RLC_FP_DIGS); fp2_nord_low(u2[0], u1[1]); fp2_addc_low(u2[0], u2[0], u0[0]); fp2_addc_low(u2[1], u2[1], u0[1]); /* d = (a + b)^2 - a^2 - b^2 = 2 * a * b. */ fp2_addc_low(u1[0], u1[0], u0[0]); fp2_addc_low(u1[1], u1[1], u0[1]); fp4_sqr_unr(u0, t); fp2_subc_low(u0[0], u0[0], u1[0]); fp2_subc_low(u0[1], u0[1], u1[1]); fp2_rdcn_low(c[0][0], u2[0]); fp2_rdcn_low(c[0][1], u2[1]); fp2_rdcn_low(c[1][0], u0[0]); fp2_rdcn_low(c[1][1], u0[1]); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { fp4_free(t); dv4_free(u0); dv4_free(u1); dv4_free(u2); } }
void fp_prime_back(bn_t c, const fp_t a) { dv_t t; int i; dv_null(t); TRY { dv_new(t); bn_grow(c, FP_DIGS); for (i = 0; i < FP_DIGS; i++) { c->dp[i] = a[i]; } #if FP_RDC == MONTY dv_zero(t, 2 * FP_DIGS + 1); dv_copy(t, a, FP_DIGS); fp_rdc(c->dp, t); #endif c->used = FP_DIGS; c->sign = BN_POS; bn_trim(c); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { dv_free(t); } }
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; }
void pp_exp_k2(fp2_t c, fp2_t a) { bn_t e, n; bn_null(n); bn_null(e); TRY { bn_new(n); bn_new(e); ep_curve_get_ord(n); fp2_conv_uni(c, a); dv_copy(e->dp, fp_prime_get(), FP_DIGS); e->used = FP_DIGS; e->sign = BN_POS; bn_add_dig(e, e, 1); bn_div(e, e, n); fp2_exp_uni(c, c, e); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { bn_free(n); bn_free(e); } }
void fp_prime_conv_dig(fp_t c, dig_t a) { dv_t t; ctx_t *ctx = core_get(); bn_null(t); TRY { dv_new(t); #if FP_RDC == MONTY if (a != 1) { dv_zero(t, 2 * FP_DIGS + 1); t[FP_DIGS] = fp_mul1_low(t, ctx->conv.dp, a); fp_rdc(c, t); } else { dv_copy(c, ctx->one.dp, FP_DIGS); } #else (void)ctx; fp_zero(c); c[0] = a; #endif } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { dv_free(t); } }
void fp_hlvm_low(dig_t *c, const dig_t *a) { dig_t carry = 0; if (a[0] & 1) { carry = fp_addn_low(c, a, fp_prime_get()); } else { dv_copy(c, a, FP_DIGS); } fp_rsh1_low(c, c); if (carry) { c[FP_DIGS - 1] ^= ((dig_t)1 << (FP_DIGIT - 1)); } }
void fp_invn_low(dig_t *c, const dig_t *a) { bn_st e; bn_init(&e, RLC_FP_DIGS); e.used = RLC_FP_DIGS; dv_copy(e.dp, fp_prime_get(), RLC_FP_DIGS); bn_sub1_low(e.dp, e.dp, 2, RLC_FP_DIGS); #if AUTO == ALLOC fp_exp(c, a, &e); #else fp_exp(c, (const fp_t)a, &e); #endif bn_clean(&e); }
void fp_prime_conv(fp_t c, const bn_t a) { bn_t t; bn_null(t); TRY { bn_new(t); #if FP_RDC == MONTY bn_mod(t, a, &(core_get()->prime)); bn_lsh(t, t, FP_DIGS * FP_DIGIT); bn_mod(t, t, &(core_get()->prime)); dv_copy(c, t->dp, FP_DIGS); #else if (a->used > FP_DIGS) { THROW(ERR_NO_PRECI); } bn_mod(t, a, &(core_get()->prime)); if (bn_is_zero(t)) { fp_zero(c); } else { int i; for (i = 0; i < t->used; i++) { c[i] = t->dp[i]; } for (; i < FP_DIGS; i++) { c[i] = 0; } } (void)t; #endif } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { bn_free(t); } }
void fp_copy(fp_t c, const fp_t a) { dv_copy(c, a, RLC_FP_DIGS); }
void fp_rdcs_low(dig_t *c, dig_t *a, dig_t *m) { align dig_t q[2 * FP_DIGS], _q[2 * FP_DIGS]; align dig_t _r[2 * FP_DIGS], r[2 * FP_DIGS], t[2 * FP_DIGS]; int *sform, len; int first, i, j, b0, d0, b1, d1; dig_t carry; sform = fp_prime_get_sps(&len); SPLIT(b0, d0, FP_BITS, FP_DIG_LOG); first = (d0) + (b0 == 0 ? 0 : 1); /* q = floor(a/b^k) */ dv_zero(q, 2 * FP_DIGS); bn_rshd_low(q, a, 2 * FP_DIGS, d0); if (b0 > 0) { bn_rshb_low(q, q, 2 * FP_DIGS, b0); } /* r = a - qb^k. */ dv_copy(r, a, first); if (b0 > 0) { r[first - 1] &= MASK(b0); } carry = 0; while (!fp_is_zero(q)) { dv_zero(_q, 2 * FP_DIGS); for (i = len - 1; i > 0; i--) { j = (sform[i] < 0 ? -sform[i] : sform[i]); SPLIT(b1, d1, j, FP_DIG_LOG); dv_zero(t, 2 * FP_DIGS); bn_lshd_low(t, q, FP_DIGS, d1); if (b1 > 0) { bn_lshb_low(t, t, 2 * FP_DIGS, b1); } if (sform[i] > 0) { bn_subn_low(_q, _q, t, 2 * FP_DIGS); } else { bn_addn_low(_q, _q, t, 2 * FP_DIGS); } } if (sform[0] > 0) { bn_subn_low(_q, _q, q, 2 * FP_DIGS); } else { bn_addn_low(_q, _q, q, 2 * FP_DIGS); } bn_rshd_low(q, _q, 2 * FP_DIGS, d0); if (b0 > 0) { bn_rshb_low(q, q, 2 * FP_DIGS, b0); } dv_copy(_r, _q, first); if (b0 > 0) { _r[first - 1] &= MASK(b0); } fp_add(r, r, _r); } while (fp_cmpn_low(r, m) != CMP_LT) { fp_subn_low(r, r, m); } fp_copy(c, r); }
int fp_srt(fp_t c, const fp_t a) { bn_t e; fp_t t0; fp_t t1; int r = 0; bn_null(e); fp_null(t0); fp_null(t1); TRY { bn_new(e); fp_new(t0); fp_new(t1); /* Make e = p. */ e->used = FP_DIGS; dv_copy(e->dp, fp_prime_get(), FP_DIGS); if (fp_prime_get_mod8() == 3 || fp_prime_get_mod8() == 7) { /* Easy case, compute a^((p + 1)/4). */ bn_add_dig(e, e, 1); bn_rsh(e, e, 2); fp_exp(t0, a, e); fp_sqr(t1, t0); r = (fp_cmp(t1, a) == CMP_EQ); fp_copy(c, t0); } else { int f = 0, m = 0; /* First, check if there is a root. Compute t1 = a^((p - 1)/2). */ bn_rsh(e, e, 1); fp_exp(t0, a, e); if (fp_cmp_dig(t0, 1) != CMP_EQ) { /* Nope, there is no square root. */ r = 0; } else { r = 1; /* Find a quadratic non-residue modulo p, that is a number t2 * such that (t2 | p) = t2^((p - 1)/2)!= 1. */ do { fp_rand(t1); fp_exp(t0, t1, e); } while (fp_cmp_dig(t0, 1) == CMP_EQ); /* Write p - 1 as (e * 2^f), odd e. */ bn_lsh(e, e, 1); while (bn_is_even(e)) { bn_rsh(e, e, 1); f++; } /* Compute t2 = t2^e. */ fp_exp(t1, t1, e); /* Compute t1 = a^e, c = a^((e + 1)/2) = a^(e/2 + 1), odd e. */ bn_rsh(e, e, 1); fp_exp(t0, a, e); fp_mul(e->dp, t0, a); fp_sqr(t0, t0); fp_mul(t0, t0, a); fp_copy(c, e->dp); while (1) { if (fp_cmp_dig(t0, 1) == CMP_EQ) { break; } fp_copy(e->dp, t0); for (m = 0; (m < f) && (fp_cmp_dig(t0, 1) != CMP_EQ); m++) { fp_sqr(t0, t0); } fp_copy(t0, e->dp); for (int i = 0; i < f - m - 1; i++) { fp_sqr(t1, t1); } fp_mul(c, c, t1); fp_sqr(t1, t1); fp_mul(t0, t0, t1); f = m; } } } } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { bn_free(e); fp_free(t0); fp_free(t1); } return r; }
void fp2_nord_low(dv2_t c, dv2_t a) { dv2_t t; bn_t b; dv2_null(t); bn_null(b); TRY { dv2_new(t); bn_new(b); #if FP_PRIME == 158 fp_addc_low(t[0], a[0], a[0]); fp_addc_low(t[0], t[0], t[0]); fp_subc_low(t[0], t[0], a[1]); fp_addc_low(t[1], a[1], a[1]); fp_addc_low(t[1], t[1], t[1]); fp_addc_low(c[1], a[0], t[1]); dv_copy(c[0], t[0], 2 * FP_DIGS); #elif defined(FP_QNRES) /* If p = 3 mod 8, (1 + i) is a QNR/CNR. */ /* (a_0 + a_1 * i) * (1 + i) = (a_0 - a_1) + (a_0 + a_1) * u. */ dv_copy(t[0], a[1], 2 * FP_DIGS); fp_addc_low(c[1], a[0], a[1]); fp_subc_low(c[0], a[0], t[0]); #else switch (fp_prime_get_mod8()) { case 3: /* If p = 3 mod 8, (1 + u) is a QNR, u^2 = -1. */ /* (a_0 + a_1 * u) * (1 + u) = (a_0 - a_1) + (a_0 + a_1) * u. */ dv_copy(t[0], a[1], 2 * FP_DIGS); fp_addc_low(c[1], a[0], a[1]); fp_subc_low(c[0], a[0], t[0]); break; case 5: /* If p = 5 mod 8, (u) is a QNR. */ dv_copy(t[0], a[0], 2 * FP_DIGS); dv_zero(t[1], FP_DIGS); dv_copy(t[1] + FP_DIGS, fp_prime_get(), FP_DIGS); fp_subc_low(c[0], t[1], a[1]); for (int i = -1; i > fp_prime_get_qnr(); i--) { fp_subc_low(c[0], c[0], a[1]); } dv_copy(c[1], t[0], 2 * FP_DIGS); break; case 7: /* If p = 7 mod 8, (2^lg_4(b-1) + u) is a QNR/CNR. */ /* (a_0 + a_1 * u)(2^lg_4(b-1) + u) = * (2^lg_4(b-1)a_0 - a_1) + (a_0 + 2^lg_4(b-1)a_1 * u. */ fp2_addc_low(t, a, a); fp_prime_back(b, ep_curve_get_b()); for (int i = 1; i < bn_bits(b) / 2; i++) { fp2_addc_low(t, t, t); } fp_subc_low(c[0], t[0], a[1]); fp_addc_low(c[1], t[1], a[0]); break; default: THROW(ERR_NO_VALID); break; } #endif } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { dv2_free(t); bn_free(b); } }
void fb_invn_low(dig_t *c, const dig_t *a) { int j, d, lu, lv, lt, l1, l2, bu, bv; align dig_t _u[2 * FB_DIGS], _v[2 * FB_DIGS]; align dig_t _g1[2 * FB_DIGS], _g2[2 * FB_DIGS]; dig_t *t = NULL, *u = NULL, *v = NULL, *g1 = NULL, *g2 = NULL, carry; dv_zero(_g1, FB_DIGS + 1); dv_zero(_g2, FB_DIGS + 1); u = _u; v = _v; g1 = _g1; g2 = _g2; /* u = a, v = f, g1 = 1, g2 = 0. */ dv_copy(u, a, FB_DIGS); dv_copy(v, fb_poly_get(), FB_DIGS); g1[0] = 1; lu = lv = FB_DIGS; l1 = l2 = 1; bu = fb_bits(u); bv = FB_BITS + 1; j = bu - bv; /* While (u != 1). */ while (1) { /* If j < 0 then swap(u, v), swap(g1, g2), j = -j. */ if (j < 0) { t = u; u = v; v = t; lt = lu; lu = lv; lv = lt; t = g1; g1 = g2; g2 = t; lt = l1; l1 = l2; l2 = lt; j = -j; } SPLIT(j, d, j, FB_DIG_LOG); /* u = u + v * z^j. */ if (j > 0) { carry = fb_lsha_low(u + d, v, j, lv); u[d + lv] ^= carry; } else { fb_addd_low(u + d, u + d, v, lv); } /* g1 = g1 + g2 * z^j. */ if (j > 0) { carry = fb_lsha_low(g1 + d, g2, j, l2); l1 = (l2 + d >= l1 ? l2 + d : l1); if (carry) { g1[d + l2] ^= carry; l1 = (l2 + d >= l1 ? l1 + 1 : l1); } } else { fb_addd_low(g1 + d, g1 + d, g2, l2); l1 = (l2 + d > l1 ? l2 + d : l1); } while (u[lu - 1] == 0) lu--; while (v[lv - 1] == 0) lv--; if (lu == 1 && u[0] == 1) break; /* j = deg(u) - deg(v). */ lt = util_bits_dig(u[lu - 1]) - util_bits_dig(v[lv - 1]); j = ((lu - lv) << FB_DIG_LOG) + lt; } /* Return g1. */ fb_copy(c, g1); }
/** * 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); } }
/** * 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); } }
/** * Assigns the prime field modulus. * * @param[in] p - the new prime field modulus. */ static void fp_prime_set(const bn_t p) { dv_t s, q; bn_t t; ctx_t *ctx = core_get(); if (p->used != FP_DIGS) { THROW(ERR_NO_VALID); } dv_null(s); bn_null(t); dv_null(q); TRY { dv_new(s); bn_new(t); dv_new(q); bn_copy(&(ctx->prime), p); bn_mod_dig(&(ctx->mod8), &(ctx->prime), 8); switch (ctx->mod8) { case 3: case 7: ctx->qnr = -1; /* The current code for extensions of Fp^3 relies on qnr being * also a cubic non-residue. */ ctx->cnr = 0; break; case 1: case 5: ctx->qnr = ctx->cnr = -2; break; default: ctx->qnr = ctx->cnr = 0; THROW(ERR_NO_VALID); break; } #ifdef FP_QNRES if (ctx->mod8 != 3) { THROW(ERR_NO_VALID); } #endif #if FP_RDC == MONTY || !defined(STRIP) bn_mod_pre_monty(t, &(ctx->prime)); ctx->u = t->dp[0]; dv_zero(s, 2 * FP_DIGS); s[2 * FP_DIGS] = 1; dv_zero(q, 2 * FP_DIGS + 1); dv_copy(q, ctx->prime.dp, FP_DIGS); bn_divn_low(t->dp, ctx->conv.dp, s, 2 * FP_DIGS + 1, q, FP_DIGS); ctx->conv.used = FP_DIGS; bn_trim(&(ctx->conv)); bn_set_dig(&(ctx->one), 1); bn_lsh(&(ctx->one), &(ctx->one), ctx->prime.used * BN_DIGIT); bn_mod(&(ctx->one), &(ctx->one), &(ctx->prime)); #endif fp_prime_calc(); } CATCH_ANY { THROW(ERR_CAUGHT); } FINALLY { bn_free(t); dv_free(s); dv_free(q); } }