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
}
void fp_addc_low(dig_t *c, const dig_t *a, const dig_t *b) {
dig_t carry = fp_addd_low(c, a, b);
if (carry || (fp_cmpn_low(c + FP_DIGS, fp_prime_get()) != CMP_LT)) {
carry = fp_subn_low(c + FP_DIGS, c + FP_DIGS, fp_prime_get());
}
}
void fp_rdc_monty_basic(fp_t c, dv_t a) {
int i;
dig_t r, c0, c1, *tmp, u0;
const dig_t *p = NULL;
tmp = a;
u0 = *(fp_prime_get_rdc());
p = fp_prime_get();
c1 = 0;
for (i = 0; i < FP_DIGS; i++, tmp++) {
r = (dig_t)(*tmp * u0);
c0 = fp_mula_low(tmp, fp_prime_get(), r);
/* We must use this because the size (FP_DIGS - i) is variable. */
c1 += bn_add1_low(tmp + FP_DIGS, tmp + FP_DIGS, c0, FP_DIGS - i);
}
fp_copy(c, a + FP_DIGS);
for (i = 0; i < c1; i++) {
fp_subn_low(c, c, p);
}
if (fp_cmpn_low(c, p) != CMP_LT) {
fp_subn_low(c, c, p);
}
}
void fp_param_print(void) {
util_banner("Prime modulus:", 0);
util_print(" ");
#if ALLOC == AUTO
fp_print(fp_prime_get());
#else
fp_print((const fp_t)fp_prime_get());
#endif
}
void fp_rand(fp_t a) {
int bits, digits;
rand_bytes((uint8_t *)a, RLC_FP_DIGS * sizeof(dig_t));
RLC_RIP(bits, digits, RLC_FP_BITS);
if (bits > 0) {
dig_t mask = ((dig_t)1 << (dig_t)bits) - 1;
a[RLC_FP_DIGS - 1] &= mask;
}
while (dv_cmp(a, fp_prime_get(), RLC_FP_DIGS) != RLC_LT) {
fp_subn_low(a, a, fp_prime_get());
}
}
void fp2_mulc_low(dv2_t c, fp2_t a, fp2_t b) {
align dig_t t0[2 * FP_DIGS], t1[2 * FP_DIGS], t2[2 * FP_DIGS];
/* Karatsuba algorithm. */
/* t0 = a_0 + a_1, t1 = b_0 + b_1. */
fp_addn_low(t0, a[0], a[1]);
fp_addn_low(t1, b[0], b[1]);
/* c_0 = a_0 * b_0, c_1 = a_1 * b_1, t2 = (a_0 + a_1) * (b_0 + b_1). */
fp_muln_low(c[0], a[0], b[0]);
fp_muln_low(c[1], a[1], b[1]);
fp_muln_low(t2, t0, t1);
/* t0 = (a_0 * b_0) + (a_1 * b_1). */
fp_addd_low(t0, c[0], c[1]);
/* c_0 = (a_0 * b_0) + u^2 * (a_1 * b_1). */
fp_subd_low(c[0], c[0], c[1]);
#ifndef FP_QNRES
/* t1 = u^2 * (a_1 * b_1). */
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_subd_low(c[0], c[0], c[1]);
}
#endif
/* c_1 = (t2 - t0). */
fp_subd_low(c[1], t2, t0);
/* c_0 = c_0 + 2^N * p/4. */
bn_lshb_low(c[0] + FP_DIGS - 1, c[0] + FP_DIGS - 1, FP_DIGS + 1, 2);
fp_addn_low(c[0] + FP_DIGS, c[0] + FP_DIGS, fp_prime_get());
bn_rshb_low(c[0] + FP_DIGS - 1, c[0] + FP_DIGS - 1, FP_DIGS + 1, 2);
}
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 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 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_rdcn_low(dig_t *c, dig_t *a) {
int i;
dig_t r, c0, c1, u, *tmp;
const dig_t *m;
u = *(fp_prime_get_rdc());
m = fp_prime_get();
tmp = a;
c1 = 0;
for (i = 0; i < FP_DIGS; i++, tmp++) {
r = (dig_t)(*tmp * u);
c0 = mpn_addmul_1(tmp, m, FP_DIGS, r);
c1 += mpn_add_1(tmp + FP_DIGS, tmp + FP_DIGS, FP_DIGS - i, c0);
}
for (i = 0; i < FP_DIGS; i++, tmp++) {
c[i] = *tmp;
}
for (i = 0; i < c1; i++) {
fp_subn_low(c, c, m);
}
if (fp_cmp(c, m) != CMP_LT) {
fp_subn_low(c, c, m);
}
}
void fp_subc_low(dig_t *c, const dig_t *a, const dig_t *b) {
dig_t carry = fp_subd_low(c, a, b);
if (carry) {
fp_addn_low(c + FP_DIGS, c + FP_DIGS, fp_prime_get());
}
}
void fp_dblm_low(dig_t *c, const dig_t *a) {
int i;
dig_t carry, c0, c1, r0, r1;
carry = 0;
for (i = 0; i < FP_DIGS; i++, a++) {
r0 = (*a) + (*a);
c0 = (r0 < (*a));
r1 = r0 + carry;
c1 = (r1 < r0);
carry = c0 | c1;
c[i] = r1;
}
if (carry || (fp_cmpn_low(c, fp_prime_get()) != CMP_LT)) {
carry = fp_subn_low(c, c, fp_prime_get());
}
}
void fp_subm_low(dig_t *c, const dig_t *a, const dig_t *b) {
dig_t carry;
carry = fp_subn_low(c, a, b);
if (carry) {
fp_addn_low(c, c, fp_prime_get());
}
}
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 fp_rdcn_low(dig_t *c, dig_t *a) {
dig_t r1, *m, *tmpc;
m = fp_prime_get();
tmpc = c;
r1 = fp_rdci_low(c, a);
if (r1 || fp_cmp(c, m) != CMP_LT) {
fp_subn_low(c, c, m);
}
}
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 {
fp_copy(c, a);
}
fp_rsh1_low(c, c);
if (carry) {
c[FP_DIGS - 1] ^= ((dig_t)1 << (FP_DIGIT - 1));
}
}
void fp_rdcn_low(dig_t *c, dig_t *a) {
int i, j;
dig_t r0, r1, r2, u, v;
dig_t *m, *tmp, *tmpm, *tmpc;
dig_t t[2 * FP_DIGS] = {0};
m = fp_prime_get();
tmpc = c;
r1 = fp_rdci_low(c, a);
if (r1 || fp_cmp(c, m) != CMP_LT) {
fp_subn_low(c, c, m);
}
}
void fp_subc_low(dig_t *c, const dig_t *a, const dig_t *b) {
int i;
dig_t carry, r0, diff;
/* Zero the carry. */
carry = 0;
for (i = 0; i < 2 * FP_DIGS; i++, a++, b++) {
diff = (*a) - (*b);
r0 = diff - carry;
carry = ((*a) < (*b)) || (carry && !diff);
c[i] = r0;
}
if (carry) {
fp_addn_low(c + FP_DIGS, c + FP_DIGS, fp_prime_get());
}
}
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_hlvd_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_add1_low(c + FP_DIGS, a + FP_DIGS, carry);
carry = fp_rsh1_low(c + FP_DIGS, c + FP_DIGS);
fp_rsh1_low(c, c);
if (carry) {
c[FP_DIGS - 1] ^= ((dig_t)1 << (FP_DIGIT - 1));
}
}
void fp_rdcn_low2(dig_t *c, dig_t *a) {
int i, j;
dig_t r0, r1, r2, u;
dig_t *m, *tmp, *tmpm, *tmpc;
u = *(fp_prime_get_rdc());
m = fp_prime_get();
tmpc = c;
r0 = r1 = r2 = 0;
for (i = 0; i < FP_DIGS; i++, tmpc++, a++) {
tmp = c;
tmpm = m + i;
for (j = 0; j < i; j++, tmp++, tmpm--) {
COMBA_STEP(r2, r1, r0, *tmp, *tmpm);
}
COMBA_ADD(r2, r1, r0, *a);
*tmpc = (dig_t)(r0 * u);
COMBA_STEP(r2, r1, r0, *tmpc, *m);
r0 = r1;
r1 = r2;
r2 = 0;
}
for (i = FP_DIGS; i < 2 * FP_DIGS - 1; i++, a++) {
tmp = c + (i - FP_DIGS + 1);
tmpm = m + FP_DIGS - 1;
for (j = i - FP_DIGS + 1; j < FP_DIGS; j++, tmp++, tmpm--) {
COMBA_STEP(r2, r1, r0, *tmp, *tmpm);
}
COMBA_ADD(r2, r1, r0, *a);
c[i - FP_DIGS] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
COMBA_ADD(r2, r1, r0, *a);
c[FP_DIGS - 1] = r0;
if (r1 || fp_cmpn_low(c, m) != CMP_LT) {
fp_subn_low(c, c, m);
}
}
void fp_print(const fp_t a) {
int i;
bn_t t;
bn_null(t);
TRY {
bn_new(t);
#if FP_RDC == MONTY
if (a != fp_prime_get()) {
fp_prime_back(t, a);
} else {
bn_read_raw(t, a, RLC_FP_DIGS);
}
#else
bn_read_raw(t, a, RLC_FP_DIGS);
#endif
for (i = RLC_FP_DIGS - 1; i > 0; i--) {
if (i >= t->used) {
util_print_dig(0, 1);
} else {
util_print_dig(t->dp[i], 1);
}
util_print(" ");
}
util_print_dig(t->dp[0], 1);
util_print("\n");
} CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(t);
}
}
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 fp_rdc_quick(fp_t c, dv_t a) {
fp_rdcs_low(c, a, fp_prime_get());
}
/**
* 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_addm_low(dig_t *c, const dig_t *a, const dig_t *b) {
fp_addn_low(c, a, b);
if (fp_cmp(c, fp_prime_get()) != CMP_LT) {
fp_subn_low(c, c, fp_prime_get());
}
}
/**
* 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);
}
}
void fp_negm_low(dig_t *c, const dig_t *a) {
fp_subn_low(c, fp_prime_get(), a);
}
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);
}
}
