1 files changed, 596 insertions, 0 deletions

diff --git a/moon-abe/pbc-0.5.14/arith/montfp.c b/moon-abe/pbc-0.5.14/arith/montfp.c
new file mode 100644
index 00000000..c79bb72b
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/arith/montfp.c
@@ -0,0 +1,596 @@
+// 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);
+}