1 files changed, 447 insertions, 0 deletions

diff --git a/moon-abe/pbc-0.5.14/ecc/singular.c b/moon-abe/pbc-0.5.14/ecc/singular.c
new file mode 100644
index 00000000..95f00410
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/ecc/singular.c
@@ -0,0 +1,447 @@
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdint.h> // for intptr_t
+#include <stdlib.h>
+#include <gmp.h>
+#include "pbc_utils.h"
+#include "pbc_field.h"
+#include "pbc_curve.h"
+#include "pbc_param.h"
+#include "pbc_pairing.h"
+#include "pbc_fp.h"
+#include "pbc_memory.h"
+
+//TODO: Store as integer mod ring instead and convert at last minute?
+struct point_s {
+  int inf_flag;
+  element_t x;
+  element_t y;
+};
+typedef struct point_s *point_ptr;
+typedef struct point_s point_t[1];
+
+static void sn_init(element_ptr e) {
+  field_ptr f = e->field->data;
+  e->data = pbc_malloc(sizeof(point_t));
+  point_ptr p = e->data;
+  element_init(p->x, f);
+  element_init(p->y, f);
+  p->inf_flag = 1;
+}
+
+static void sn_clear(element_ptr e) {
+  point_ptr p = e->data;
+  element_clear(p->x);
+  element_clear(p->y);
+  pbc_free(e->data);
+}
+
+static void sn_set0(element_ptr x) {
+  point_ptr p = x->data;
+  p->inf_flag = 1;
+}
+
+static int sn_is0(element_ptr x) {
+  point_ptr p = x->data;
+  return p->inf_flag;
+}
+
+//singular with node: y^2 = x^3 + x^2
+static void sn_random(element_t a) {
+  point_ptr p = a->data;
+  element_t t;
+
+  element_init(t, p->x->field);
+  p->inf_flag = 0;
+  do {
+    element_random(p->x);
+    if (element_is0(p->x)) continue;
+    element_square(t, p->x);
+    element_add(t, t, p->x);
+    element_mul(t, t, p->x);
+  } while (!element_is_sqr(t));
+  element_sqrt(p->y, t);
+
+  element_clear(t);
+}
+
+static inline void sn_double_no_check(point_ptr r, point_ptr p) {
+  element_t lambda, e0, e1;
+
+  element_init(lambda, p->x->field);
+  element_init(e0, p->x->field);
+  element_init(e1, p->x->field);
+  //same point: double them
+
+  //lambda = (3x^2 + 2x) / 2y
+  element_mul_si(lambda, p->x, 3);
+  element_set_si(e0, 2);
+  element_add(lambda, lambda, e0);
+  element_mul(lambda, lambda, p->x);
+  element_add(e0, p->y, p->y);
+  element_invert(e0, e0);
+  element_mul(lambda, lambda, e0);
+  //x1 = lambda^2 - 2x - 1
+  element_add(e1, p->x, p->x);
+  element_square(e0, lambda);
+  element_sub(e0, e0, e1);
+  element_set_si(e1, 1);
+  element_sub(e0, e0, e1);
+  //y1 = (x - x1)lambda - y
+  element_sub(e1, p->x, e0);
+  element_mul(e1, e1, lambda);
+  element_sub(e1, e1, p->y);
+
+  element_set(r->x, e0);
+  element_set(r->y, e1);
+  r->inf_flag = 0;
+
+  element_clear(lambda);
+  element_clear(e0);
+  element_clear(e1);
+  return;
+}
+
+static void sn_double(element_t c, element_t a) {
+  point_ptr r = c->data;
+  point_ptr p = a->data;
+  if (p->inf_flag) {
+    r->inf_flag = 1;
+    return;
+  }
+  if (element_is0(p->y)) {
+    r->inf_flag = 1;
+    return;
+  }
+  sn_double_no_check(r, p);
+}
+
+static void sn_set(element_ptr c, element_ptr a) {
+  point_ptr r = c->data, p = a->data;
+  if (p->inf_flag) {
+    r->inf_flag = 1;
+    return;
+  }
+  r->inf_flag = 0;
+  element_set(r->x, p->x);
+  element_set(r->y, p->y);
+}
+
+static void sn_add(element_t c, element_t a, element_t b) {
+  point_ptr r = c->data;
+  point_ptr p = a->data;
+  point_ptr q = b->data;
+  if (p->inf_flag) {
+    sn_set(c, b);
+    return;
+  }
+  if (q->inf_flag) {
+    sn_set(c, a);
+    return;
+  }
+  if (!element_cmp(p->x, q->x)) {
+    if (!element_cmp(p->y, q->y)) {
+      if (element_is0(p->y)) {
+        r->inf_flag = 1;
+        return;
+      } else {
+        sn_double_no_check(r, p);
+        return;
+      }
+    }
+    //points are inverses of each other
+    r->inf_flag = 1;
+    return;
+  } else {
+    element_t lambda, e0, e1;
+
+    element_init(lambda, p->x->field);
+    element_init(e0, p->x->field);
+    element_init(e1, p->x->field);
+
+    //lambda = (y2-y1)/(x2-x1)
+    element_sub(e0, q->x, p->x);
+    element_invert(e0, e0);
+    element_sub(lambda, q->y, p->y);
+    element_mul(lambda, lambda, e0);
+    //x3 = lambda^2 - x1 - x2 - 1
+    element_square(e0, lambda);
+    element_sub(e0, e0, p->x);
+    element_sub(e0, e0, q->x);
+    element_set1(e1);
+    element_sub(e0, e0, e1);
+    //y3 = (x1-x3)lambda - y1
+    element_sub(e1, p->x, e0);
+    element_mul(e1, e1, lambda);
+    element_sub(e1, e1, p->y);
+
+    element_set(r->x, e0);
+    element_set(r->y, e1);
+    r->inf_flag = 0;
+
+    element_clear(lambda);
+    element_clear(e0);
+    element_clear(e1);
+  }
+}
+
+static void sn_invert(element_ptr c, element_ptr a) {
+  point_ptr r = c->data, p = a->data;
+
+  if (p->inf_flag) {
+    r->inf_flag = 1;
+    return;
+  }
+  r->inf_flag = 0;
+  element_set(r->x, p->x);
+  element_neg(r->y, p->y);
+}
+
+static void sn_field_clear(field_ptr c) {
+  UNUSED_VAR(c);
+}
+
+/* TODO: Write a test program that uses these functions.
+
+// Nonsingular points on sn curves map to finite field elements via
+//   (x, y) --> (y + x)/(y - x)
+// The reverse map is
+//   a --> (4a/(a-1)^2, 4a(a+1)/(a-1)^3)
+
+void sn_point_to_field(element_t out, point_ptr P) {
+  element_t e0, e1;
+  if (P->inf_flag) {
+    element_set1(out);
+    return;
+  }
+  element_init(e0, out->field);
+  element_init(e1, out->field);
+  element_add(e0, P->y, P->x);
+  element_sub(e1, P->y, P->x);
+  element_invert(e1, e1);
+  element_mul(out, e0, e1);
+  element_clear(e0);
+  element_clear(e1);
+}
+
+static void sn_field_to_point(point_ptr P, element_t in) {
+  element_t e0, e1, e2;
+
+  if (element_is1(in)) {
+    P->inf_flag = 1;
+    return;
+  }
+  element_init(e0, in->field);
+  element_init(e1, in->field);
+  element_init(e2, in->field);
+
+  element_set1(e1);
+  element_sub(e0, in, e1);
+  element_invert(e0, e0);
+
+  element_mul_si(e2, in, 4);
+
+  element_add(P->y, in, e1);
+
+  element_mul(e1, e0, e0);
+  element_mul(P->x, e1, e2);
+  element_mul(P->y, P->y, e2);
+  element_mul(P->y, P->y, e0);
+  element_mul(P->y, P->y, e1);
+  P->inf_flag = 0;
+
+  element_clear(e0);
+  element_clear(e1);
+  element_clear(e2);
+}
+*/
+
+static size_t sn_out_str(FILE *stream, int base, element_ptr a) {
+  point_ptr p = a->data;
+  size_t result, status;
+  if (p->inf_flag) {
+    if (EOF == fputc('O', stream)) return 0;
+    return 1;
+  }
+  result = element_out_str(stream, base, p->x);
+  if (!result) return 0;
+  if (EOF == fputc(' ', stream)) return 0;
+  status = element_out_str(stream, base, p->y);
+  if (!status) return 0;
+  return result + status + 1;
+}
+
+void naive_generic_pow_mpz(element_ptr x, element_ptr a, mpz_ptr n);
+void field_init_curve_singular_with_node(field_t c, field_t field) {
+  mpz_set(c->order, field->order);
+  c->data = (void *) field;
+  c->init = sn_init;
+  c->clear = sn_clear;
+  c->random = sn_random;
+  //c->from_x = cc_from_x;
+  //c->from_hash = cc_from_hash;
+  c->set = sn_set;
+  c->invert = c->neg = sn_invert;
+  c->square = c->doub = sn_double;
+  c->mul = c->add = sn_add;
+  c->set1 = c->set0 = sn_set0;
+  c->is1 = c->is0 = sn_is0;
+  c->mul_mpz = element_pow_mpz;
+  c->out_str = sn_out_str;
+  c->field_clear = sn_field_clear;
+}
+
+//TODO: the following code is useless as the Tate pairing is degenerate on singular curves
+static void sn_miller(element_t res, mpz_t q, element_t P,
+    element_ptr Qx, element_ptr Qy) {
+  //collate divisions
+  int m;
+  element_t v, vd;
+  element_t Z;
+  element_t a, b, c;
+  element_t e0, e1;
+  element_ptr Zx;
+  element_ptr Zy;
+  const element_ptr Px = curve_x_coord(P);
+  const element_ptr Py = curve_y_coord(P);
+
+  #define do_vertical(e)     \
+    element_sub(e0, Qx, Zx); \
+    element_mul(e, e, e0);
+
+  //a = -slope_tangent(Z.x, Z.y);
+  //b = 1;
+  //c = -(Z.y + a * Z.x);
+  //but we multiply by 2*Z.y to avoid division
+  //a = -Zx * (Zx + Zx + Zx + 2)
+  //b = 2 * Zy
+  //c = -(2 Zy^2 + a Zx);
+  #define do_tangent(e)      \
+    element_double(e0, Zx);  \
+    element_add(a, Zx, e0);  \
+    element_set_si(e0, 2);   \
+    element_add(a, a, e0);   \
+    element_mul(a, a, Zx);   \
+    element_neg(a, a);       \
+    element_add(b, Zy, Zy);  \
+    element_mul(e0, b, Zy);  \
+    element_mul(c, a, Zx);   \
+    element_add(c, c, e0);   \
+    element_neg(c, c);       \
+    element_mul(e0, a, Qx);  \
+    element_mul(e1, b, Qy);  \
+    element_add(e0, e0, e1); \
+    element_add(e0, e0, c);  \
+    element_mul(e, e, e0);
+
+  //a = -(B.y - A.y) / (B.x - A.x);
+  //b = 1;
+  //c = -(A.y + a * A.x);
+  //but we'll multiply by B.x - A.x to avoid division
+  #define do_line(e)         \
+    element_sub(b, Px, Zx);  \
+    element_sub(a, Zy, Py);  \
+    element_mul(e0, b, Zy);  \
+    element_mul(c, a, Zx);   \
+    element_add(c, c, e0);   \
+    element_neg(c, c);       \
+    element_mul(e0, a, Qx);  \
+    element_mul(e1, b, Qy);  \
+    element_add(e0, e0, e1); \
+    element_add(e0, e0, c);  \
+    element_mul(e, e, e0);
+
+  element_init(a, Px->field);
+  element_init(b, Px->field);
+  element_init(c, Px->field);
+  element_init(e0, res->field);
+  element_init(e1, res->field);
+
+  element_init(v, res->field);
+  element_init(vd, res->field);
+  element_init(Z, P->field);
+
+  element_set(Z, P);
+  Zx = curve_x_coord(Z);
+  Zy = curve_y_coord(Z);
+
+  element_set1(v);
+  element_set1(vd);
+  m = mpz_sizeinbase(q, 2) - 2;
+
+  while(m >= 0) {
+    element_mul(v, v, v);
+    element_mul(vd, vd, vd);
+    do_tangent(v);
+    element_double(Z, Z);
+    do_vertical(vd);
+    if (mpz_tstbit(q, m)) {
+      do_line(v);
+      element_add(Z, Z, P);
+      do_vertical(vd);
+    }
+    m--;
+  }
+  #undef do_tangent
+  #undef do_vertical
+  #undef do_line
+
+  element_invert(vd, vd);
+  element_mul(res, v, vd);
+
+  element_clear(v);
+  element_clear(vd);
+  element_clear(Z);
+  element_clear(a);
+  element_clear(b);
+  element_clear(c);
+  element_clear(e0);
+  element_clear(e1);
+}
+
+struct sn_pairing_data_s {
+  field_t Fq, Eq;
+};
+typedef struct sn_pairing_data_s sn_pairing_data_t[1];
+typedef struct sn_pairing_data_s *sn_pairing_data_ptr;
+
+static void sn_pairing(element_ptr out, element_ptr in1, element_ptr in2,
+    pairing_t pairing) {
+  sn_pairing_data_ptr p = pairing->data;
+  element_ptr Q = in2;
+  element_t e0;
+  element_t R, QR;
+  element_init(R, p->Eq);
+  element_init(QR, p->Eq);
+  element_random(R);
+  element_init(e0, out->field);
+  element_add(QR, Q, R);
+  sn_miller(out, pairing->r, in1, curve_x_coord(QR), curve_y_coord(QR));
+  sn_miller(e0, pairing->r, in1, curve_x_coord(R), curve_y_coord(R));
+  element_invert(e0, e0);
+  element_mul(out, out, e0);
+  //element_pow_mpz(out, out, p->tateexp);
+  element_clear(R);
+  element_clear(QR);
+}
+
+void pairing_init_singular_with_node(pairing_t pairing, mpz_t q) {
+  sn_pairing_data_ptr p;
+
+  mpz_init(pairing->r);
+  mpz_sub_ui(pairing->r, q, 1);
+  field_init_fp(pairing->Zr, pairing->r);
+  pairing->map = sn_pairing;
+
+  p = pairing->data = pbc_malloc(sizeof(sn_pairing_data_t));
+  field_init_fp(p->Fq, q);
+  field_init_curve_singular_with_node(p->Eq, p->Fq);
+
+  //mpz_init(p->tateexp);
+  //mpz_sub_ui(p->tateexp, p->Fq->order, 1);
+  //mpz_divexact(p->tateexp, p->tateexp, pairing->r);
+
+  pairing->G2 = pairing->G1 = p->Eq;
+
+  pairing_GT_init(pairing, p->Fq);
+}