diff options
Diffstat (limited to 'moon-abe/pbc-0.5.14/arith/montfp.c')
-rw-r--r-- | moon-abe/pbc-0.5.14/arith/montfp.c | 596 |
1 files changed, 0 insertions, 596 deletions
diff --git a/moon-abe/pbc-0.5.14/arith/montfp.c b/moon-abe/pbc-0.5.14/arith/montfp.c deleted file mode 100644 index c79bb72b..00000000 --- a/moon-abe/pbc-0.5.14/arith/montfp.c +++ /dev/null @@ -1,596 +0,0 @@ -// F_p using Montgomery representation. -// -// Let b = 256^sizeof(mp_limb_t). -// Let R = b^t be the smallest power of b greater than the modulus p. -// Then x is stored as xR (mod p). -// Addition: same as naive implementation. -// Multipication: Montgomery reduction. -// Code assumes the modulus p is odd. -// -// TODO: mul_2exp(x, p->bytes * 8) could be replaced with -// faster code that messes with GMP internals - -#include <stdarg.h> -#include <stdio.h> -#include <stdint.h> // for intptr_t -#include <stdlib.h> -#include <string.h> -#include <gmp.h> -#include "pbc_utils.h" -#include "pbc_field.h" -#include "pbc_random.h" -#include "pbc_fp.h" -#include "pbc_memory.h" - -// Per-field data. -typedef struct { - size_t limbs; // Number of limbs per element. - size_t bytes; // Number of bytes per element. - mp_limb_t *primelimbs; // Points to an array of limbs holding the modulus. - mp_limb_t negpinv; // -p^-1 mod b - mp_limb_t *R; // R mod p - mp_limb_t *R3; // R^3 mod p -} *fptr; - -// Per-element data. -typedef struct { - char flag; // flag == 0 means the element is zero. - mp_limb_t *d; // Otherwise d points to an array holding the element. -} *eptr; - -// Copies limbs of z into dst and zeroes any leading limbs, where n is the -// total number of limbs. -// Requires z to have at most n limbs. -static inline void set_limbs(mp_limb_t *dst, mpz_t z, size_t n) { - size_t count; - mpz_export(dst, &count, -1, sizeof(mp_limb_t), 0, 0, z); - memset((void *) (((unsigned char *) dst) + count * sizeof(mp_limb_t)), - 0, (n - count) * sizeof(mp_limb_t)); -} - -static void fp_init(element_ptr e) { - fptr p = e->field->data; - eptr ep = e->data = pbc_malloc(sizeof(*ep)); - ep->flag = 0; - ep->d = pbc_malloc(p->bytes); -} - -static void fp_clear(element_ptr e) { - eptr ep = e->data; - pbc_free(ep->d); - pbc_free(e->data); -} - -static void fp_set_mpz(element_ptr e, mpz_ptr z) { - fptr p = e->field->data; - eptr ep = e->data; - if (!mpz_sgn(z)) ep->flag = 0; - else { - mpz_t tmp; - mpz_init(tmp); - mpz_mul_2exp(tmp, z, p->bytes * 8); - mpz_mod(tmp, tmp, e->field->order); - if (!mpz_sgn(tmp)) ep->flag = 0; - else { - set_limbs(ep->d, tmp, p->limbs); - ep->flag = 2; - } - mpz_clear(tmp); - } -} - -static void fp_set_si(element_ptr e, signed long int op) { - fptr p = e->field->data; - eptr ep = e->data; - if (!op) ep->flag = 0; - else { - mpz_t tmp; - mpz_init(tmp); - // TODO: Could be optimized. - mpz_set_si(tmp, op); - mpz_mul_2exp(tmp, tmp, p->bytes * 8); - mpz_mod(tmp, tmp, e->field->order); - if (!mpz_sgn(tmp)) ep->flag = 0; - else { - set_limbs(ep->d, tmp, p->limbs); - ep->flag = 2; - } - mpz_clear(tmp); - } -} - -// Montgomery reduction. -// Algorithm II.4 from Blake, Seroussi and Smart. -static void mont_reduce(mp_limb_t *x, mp_limb_t *y, fptr p) { - size_t t = p->limbs; - size_t i; - mp_limb_t flag = 0; - for (i = 0; i < t; i++) { - mp_limb_t u = y[i] * p->negpinv; - mp_limb_t carry = mpn_addmul_1(&y[i], p->primelimbs, t, u); - //mpn_add_1(&y[i+t], &y[i+t], t - i + 1, carry); - flag += mpn_add_1(&y[i + t], &y[i + t], t - i, carry); - } - if (flag || mpn_cmp(&y[t], p->primelimbs, t) >= 0) { - mpn_sub_n(x, &y[t], p->primelimbs, t); - } else { - // TODO: GMP set might be faster. - memcpy(x, &y[t], t * sizeof(mp_limb_t)); - } -} - -static void fp_to_mpz(mpz_ptr z, element_ptr e) { - eptr ep = e->data; - if (!ep->flag) mpz_set_ui(z, 0); - else { - // x is stored as xR. - // We must divide out R to convert to standard representation. - fptr p = e->field->data; - mp_limb_t tmp[2 * p->limbs]; - - memcpy(tmp, ep->d, p->limbs * sizeof(mp_limb_t)); - memset(&tmp[p->limbs], 0, p->limbs * sizeof(mp_limb_t)); - _mpz_realloc(z, p->limbs); - mont_reduce(z->_mp_d, tmp, p); - // Remove leading zero limbs. - for (z->_mp_size = p->limbs; !z->_mp_d[z->_mp_size - 1]; z->_mp_size--); - } -} - -static void fp_set0(element_ptr e) { - eptr ep = e->data; - ep->flag = 0; -} - -static void fp_set1(element_ptr e) { - fptr p = e->field->data; - eptr ep = e->data; - ep->flag = 2; - memcpy(ep->d, p->R, p->bytes); -} - -static int fp_is1(element_ptr e) { - eptr ep = e->data; - if (!ep->flag) return 0; - else { - fptr p = e->field->data; - return !mpn_cmp(ep->d, p->R, p->limbs); - } -} - -static int fp_is0(element_ptr e) { - eptr ep = e->data; - return !ep->flag; -} - -static size_t fp_out_str(FILE * stream, int base, element_ptr e) { - size_t result; - mpz_t z; - mpz_init(z); - fp_to_mpz(z, e); - result = mpz_out_str(stream, base, z); - mpz_clear(z); - return result; -} - -static int fp_snprint(char *s, size_t n, element_ptr e) { - int result; - mpz_t z; - mpz_init(z); - fp_to_mpz(z, e); - result = gmp_snprintf(s, n, "%Zd", z); - mpz_clear(z); - return result; -} - -static int fp_set_str(element_ptr e, const char *s, int base) { - mpz_t z; - mpz_init(z); - int result = pbc_mpz_set_str(z, s, base); - mpz_mod(z, z, e->field->order); - fp_set_mpz(e, z); - mpz_clear(z); - return result; -} - -static void fp_set(element_ptr c, element_ptr a) { - eptr ad = a->data; - eptr cd = c->data; - if (a == c) return; - if (!ad->flag) cd->flag = 0; - else { - fptr p = a->field->data; - - // Assembly is faster, but I don't want to stoop to that level. - // Instead of memcpy(), we rewrite so GMP assembly ends up being invoked. - /* - memcpy(cd->d, ad->d, p->bytes); - */ - mpz_t z1, z2; - z1->_mp_d = cd->d; - z2->_mp_d = ad->d; - z1->_mp_size = z1->_mp_alloc = z2->_mp_size = z2->_mp_alloc = p->limbs; - mpz_set(z1, z2); - - cd->flag = 2; - } -} - -static void fp_add(element_ptr c, element_ptr a, element_ptr b) { - eptr ad = a->data, bd = b->data; - - if (!ad->flag) { - fp_set(c, b); - } else if (!bd->flag) { - fp_set(c, a); - } else { - eptr cd = c->data; - fptr p = a->field->data; - const size_t t = p->limbs; - mp_limb_t carry; - carry = mpn_add_n(cd->d, ad->d, bd->d, t); - - if (carry) { - // Assumes result of following sub is not zero, - // i.e. modulus cannot be 2^(n * bits_per_limb). - mpn_sub_n(cd->d, cd->d, p->primelimbs, t); - cd->flag = 2; - } else { - int i = mpn_cmp(cd->d, p->primelimbs, t); - if (!i) { - cd->flag = 0; - } else { - cd->flag = 2; - if (i > 0) { - mpn_sub_n(cd->d, cd->d, p->primelimbs, t); - } - } - } - } -} - -static void fp_double(element_ptr c, element_ptr a) { - eptr ad = a->data, cd = c->data; - if (!ad->flag) { - cd->flag = 0; - } else { - fptr p = c->field->data; - const size_t t = p->limbs; - if (mpn_lshift(cd->d, ad->d, t, 1)) { - cd->flag = 2; - // Again, assumes result is not zero. - mpn_sub_n(cd->d, cd->d, p->primelimbs, t); - } else { - int i = mpn_cmp(cd->d, p->primelimbs, t); - if (!i) { - cd->flag = 0; - } else { - cd->flag = 2; - if (i > 0) { - mpn_sub_n(cd->d, cd->d, p->primelimbs, t); - } - } - } - } -} - -static void fp_halve(element_ptr c, element_ptr a) { - eptr ad = a->data, cd = c->data; - if (!ad->flag) { - cd->flag = 0; - } else { - fptr p = c->field->data; - const size_t t = p->limbs; - int carry = 0; - mp_limb_t *alimb = ad->d; - mp_limb_t *climb = cd->d; - if (alimb[0] & 1) { - carry = mpn_add_n(climb, alimb, p->primelimbs, t); - } else fp_set(c, a); - - mpn_rshift(climb, climb, t, 1); - if (carry) climb[t - 1] |= ((mp_limb_t) 1) << (sizeof(mp_limb_t) * 8 - 1); - } -} - -static void fp_neg(element_ptr c, element_ptr a) { - eptr ad = a->data, cd = c->data; - if (!ad->flag) cd->flag = 0; - else { - fptr p = a->field->data; - mpn_sub_n(cd->d, p->primelimbs, ad->d, p->limbs); - cd->flag = 2; - } -} - -static void fp_sub(element_ptr c, element_ptr a, element_ptr b) { - eptr ad = a->data, bd = b->data; - - if (!ad->flag) { - fp_neg(c, b); - } else if (!bd->flag) { - fp_set(c, a); - } else { - fptr p = c->field->data; - size_t t = p->limbs; - eptr cd = c->data; - int i = mpn_cmp(ad->d, bd->d, t); - - if (i == 0) { - cd->flag = 0; - } else { - cd->flag = 2; - mpn_sub_n(cd->d, ad->d, bd->d, t); - if (i < 0) { - mpn_add_n(cd->d, cd->d, p->primelimbs, t); - } - } - } -} - -// Montgomery multiplication. -// See Blake, Seroussi and Smart. -static inline void mont_mul(mp_limb_t *c, mp_limb_t *a, mp_limb_t *b, - fptr p) { - // Instead of right shifting every iteration - // I allocate more room for the z array. - size_t i, t = p->limbs; - mp_limb_t z[2 * t + 1]; - mp_limb_t u = (a[0] * b[0]) * p->negpinv; - mp_limb_t v = z[t] = mpn_mul_1(z, b, t, a[0]); - z[t] += mpn_addmul_1(z, p->primelimbs, t, u); - z[t + 1] = z[t] < v; // Handle overflow. - for (i = 1; i < t; i++) { - u = (z[i] + a[i] * b[0]) * p->negpinv; - v = z[t + i] += mpn_addmul_1(z + i, b, t, a[i]); - z[t + i] += mpn_addmul_1(z + i, p->primelimbs, t, u); - z[t + i + 1] = z[t + i] < v; - } - if (z[t * 2] || mpn_cmp(z + t, p->primelimbs, t) >= 0) { - mpn_sub_n(c, z + t, p->primelimbs, t); - } else { - memcpy(c, z + t, t * sizeof(mp_limb_t)); - // Doesn't seem to make a difference: - /* - mpz_t z1, z2; - z1->_mp_d = c; - z2->_mp_d = z + t; - z1->_mp_size = z1->_mp_alloc = z2->_mp_size = z2->_mp_alloc = t; - mpz_set(z1, z2); - */ - } -} - -static void fp_mul(element_ptr c, element_ptr a, element_ptr b) { - eptr ad = a->data, bd = b->data; - eptr cd = c->data; - - if (!ad->flag || !bd->flag) { - cd->flag = 0; - } else { - fptr p = c->field->data; - mont_mul(cd->d, ad->d, bd->d, p); - cd->flag = 2; - } -} - -static void fp_pow_mpz(element_ptr c, element_ptr a, mpz_ptr op) { - // Alternative: rewrite GMP mpz_powm(). - fptr p = a->field->data; - eptr ad = a->data; - eptr cd = c->data; - if (!ad->flag) cd->flag = 0; - else { - mpz_t z; - mpz_init(z); - fp_to_mpz(z, a); - mpz_powm(z, z, op, a->field->order); - mpz_mul_2exp(z, z, p->bytes * 8); - mpz_mod(z, z, a->field->order); - set_limbs(cd->d, z, p->limbs); - mpz_clear(z); - cd->flag = 2; - } -} - -// Inversion is slower than in a naive Fp implementation because of an extra -// multiplication. -// Requires nonzero a. -static void fp_invert(element_ptr c, element_ptr a) { - eptr ad = a->data; - eptr cd = c->data; - fptr p = a->field->data; - mp_limb_t tmp[p->limbs]; - mpz_t z; - - mpz_init(z); - - // Copy the limbs into a regular mpz_t so we can invert using the standard - // mpz_invert(). - mpz_import(z, p->limbs, -1, sizeof(mp_limb_t), 0, 0, ad->d); - mpz_invert(z, z, a->field->order); - set_limbs(tmp, z, p->limbs); - - // Normalize. - mont_mul(cd->d, tmp, p->R3, p); - cd->flag = 2; - mpz_clear(z); -} - -static void fp_random(element_ptr a) { - fptr p = a->field->data; - eptr ad = a->data; - mpz_t z; - mpz_init(z); - pbc_mpz_random(z, a->field->order); - if (mpz_sgn(z)) { - mpz_mul_2exp(z, z, p->bytes * 8); - mpz_mod(z, z, a->field->order); - set_limbs(ad->d, z, p->limbs); - ad->flag = 2; - } else { - ad->flag = 0; - } - mpz_clear(z); -} - -static void fp_from_hash(element_ptr a, void *data, int len) { - mpz_t z; - - mpz_init(z); - pbc_mpz_from_hash(z, a->field->order, data, len); - fp_set_mpz(a, z); - mpz_clear(z); -} - -static int fp_cmp(element_ptr a, element_ptr b) { - eptr ad = a->data, bd = b->data; - if (!ad->flag) return bd->flag; - else { - fptr p = a->field->data; - return mpn_cmp(ad->d, bd->d, p->limbs); - //return memcmp(ad->d, bd->d, p->limbs); - } -} - -static int fp_sgn_odd(element_ptr a) { - eptr ad = a->data; - if (!ad->flag) return 0; - else { - mpz_t z; - mpz_init(z); - int res; - fp_to_mpz(z, a); - res = mpz_odd_p(z) ? 1 : -1; - mpz_clear(z); - return res; - } -} - -static int fp_is_sqr(element_ptr a) { - eptr ad = a->data; - int res; - mpz_t z; - mpz_init(z); - // 0 is a square. - if (!ad->flag) return 1; - fp_to_mpz(z, a); - res = mpz_legendre(z, a->field->order) == 1; - mpz_clear(z); - return res; -} - -static int fp_to_bytes(unsigned char *data, element_t a) { - mpz_t z; - int n = a->field->fixed_length_in_bytes; - - mpz_init(z); - fp_to_mpz(z, a); - pbc_mpz_out_raw_n(data, n, z); - mpz_clear(z); - return n; -} - -static int fp_from_bytes(element_t a, unsigned char *data) { - fptr p = a->field->data; - eptr ad = a->data; - int n; - mpz_t z; - - mpz_init(z); - - n = a->field->fixed_length_in_bytes; - mpz_import(z, n, 1, 1, 1, 0, data); - if (!mpz_sgn(z)) ad->flag = 0; - else { - ad->flag = 2; - mpz_mul_2exp(z, z, p->bytes * 8); - mpz_mod(z, z, a->field->order); - set_limbs(ad->d, z, p->limbs); - } - mpz_clear(z); - return n; -} - -static void fp_field_clear(field_t f) { - fptr p = f->data; - pbc_free(p->primelimbs); - pbc_free(p->R); - pbc_free(p->R3); - pbc_free(p); -} - -// The only public functions. All the above should be static. - -static void fp_out_info(FILE * out, field_ptr f) { - element_fprintf(out, "GF(%Zd): Montgomery representation", f->order); -} - -void field_init_mont_fp(field_ptr f, mpz_t prime) { - PBC_ASSERT(!mpz_fits_ulong_p(prime), "modulus too small"); - fptr p; - field_init(f); - f->init = fp_init; - f->clear = fp_clear; - f->set_si = fp_set_si; - f->set_mpz = fp_set_mpz; - f->out_str = fp_out_str; - f->snprint = fp_snprint; - f->set_str = fp_set_str; - f->add = fp_add; - f->sub = fp_sub; - f->set = fp_set; - f->mul = fp_mul; - f->doub = fp_double; - f->halve = fp_halve; - f->pow_mpz = fp_pow_mpz; - f->neg = fp_neg; - f->sign = fp_sgn_odd; - f->cmp = fp_cmp; - f->invert = fp_invert; - f->random = fp_random; - f->from_hash = fp_from_hash; - f->is1 = fp_is1; - f->is0 = fp_is0; - f->set0 = fp_set0; - f->set1 = fp_set1; - f->is_sqr = fp_is_sqr; - f->sqrt = element_tonelli; - f->field_clear = fp_field_clear; - f->to_bytes = fp_to_bytes; - f->from_bytes = fp_from_bytes; - f->to_mpz = fp_to_mpz; - f->out_info = fp_out_info; - - // Initialize per-field data specific to this implementation. - p = f->data = pbc_malloc(sizeof(*p)); - p->limbs = mpz_size(prime); - p->bytes = p->limbs * sizeof(mp_limb_t); - p->primelimbs = pbc_malloc(p->bytes); - mpz_export(p->primelimbs, &p->limbs, -1, sizeof(mp_limb_t), 0, 0, prime); - - mpz_set(f->order, prime); - f->fixed_length_in_bytes = (mpz_sizeinbase(prime, 2) + 7) / 8; - - // Compute R, R3 and negpinv. - mpz_t z; - mpz_init(z); - - p->R = pbc_malloc(p->bytes); - p->R3 = pbc_malloc(p->bytes); - mpz_setbit(z, p->bytes * 8); - mpz_mod(z, z, prime); - set_limbs(p->R, z, p->limbs); - - mpz_powm_ui(z, z, 3, prime); - set_limbs(p->R3, z, p->limbs); - - mpz_set_ui(z, 0); - - // Algorithm II.5 in Blake, Seroussi and Smart is better but this suffices - // since we're only doing it once. - mpz_setbit(z, p->bytes * 8); - mpz_invert(z, prime, z); - p->negpinv = -mpz_get_ui(z); - mpz_clear(z); -} |