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-rw-r--r--moon-abe/pbc-0.5.14/arith/montfp.c596
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);
-}