1  /***********************************************************************
  2   * Copyright (c) Pieter Wuille, Gregory Maxwell, Peter Dettman         *
  3   * Distributed under the MIT software license, see the accompanying    *
  4   * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
  5   ***********************************************************************/
  6  
  7  #ifndef SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H
  8  #define SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H
  9  
 10  #include "ecmult_gen_compute_table.h"
 11  #include "group_impl.h"
 12  #include "field_impl.h"
 13  #include "scalar_impl.h"
 14  #include "ecmult_gen.h"
 15  #include "util.h"
 16  
 17  static void secp256k1_ecmult_gen_compute_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int blocks, int teeth, int spacing) {
 18      size_t points = ((size_t)1) << (teeth - 1);
 19      size_t points_total = points * blocks;
 20      secp256k1_ge* prec = checked_malloc(&default_error_callback, points_total * sizeof(*prec));
 21      secp256k1_gej* ds = checked_malloc(&default_error_callback, teeth * sizeof(*ds));
 22      secp256k1_gej* vs = checked_malloc(&default_error_callback, points_total * sizeof(*vs));
 23      secp256k1_gej u;
 24      size_t vs_pos = 0;
 25      secp256k1_scalar half;
 26      int block, i;
 27  
 28      VERIFY_CHECK(points_total > 0);
 29  
 30      /* u is the running power of two times gen we're working with, initially gen/2. */
 31      secp256k1_scalar_half(&half, &secp256k1_scalar_one);
 32      secp256k1_gej_set_infinity(&u);
 33      for (i = 255; i >= 0; --i) {
 34          /* Use a very simple multiplication ladder to avoid dependency on ecmult. */
 35          secp256k1_gej_double_var(&u, &u, NULL);
 36          if (secp256k1_scalar_get_bits_limb32(&half, i, 1)) {
 37              secp256k1_gej_add_ge_var(&u, &u, gen, NULL);
 38          }
 39      }
 40  #ifdef VERIFY
 41      {
 42          /* Verify that u*2 = gen. */
 43          secp256k1_gej double_u;
 44          secp256k1_gej_double_var(&double_u, &u, NULL);
 45          VERIFY_CHECK(secp256k1_gej_eq_ge_var(&double_u, gen));
 46      }
 47  #endif
 48  
 49      for (block = 0; block < blocks; ++block) {
 50          int tooth;
 51          /* Here u = 2^(block*teeth*spacing) * gen/2. */
 52          secp256k1_gej sum;
 53          secp256k1_gej_set_infinity(&sum);
 54          for (tooth = 0; tooth < teeth; ++tooth) {
 55              /* Here u = 2^((block*teeth + tooth)*spacing) * gen/2. */
 56              /* Make sum = sum(2^((block*teeth + t)*spacing), t=0..tooth) * gen/2. */
 57              secp256k1_gej_add_var(&sum, &sum, &u, NULL);
 58              /* Make u = 2^((block*teeth + tooth)*spacing + 1) * gen/2. */
 59              secp256k1_gej_double_var(&u, &u, NULL);
 60              /* Make ds[tooth] = u = 2^((block*teeth + tooth)*spacing + 1) * gen/2. */
 61              ds[tooth] = u;
 62              /* Make u = 2^((block*teeth + tooth + 1)*spacing) * gen/2, unless at the end. */
 63              if (block + tooth != blocks + teeth - 2) {
 64                  int bit_off;
 65                  for (bit_off = 1; bit_off < spacing; ++bit_off) {
 66                      secp256k1_gej_double_var(&u, &u, NULL);
 67                  }
 68              }
 69          }
 70          /* Now u = 2^((block*teeth + teeth)*spacing) * gen/2
 71           *       = 2^((block+1)*teeth*spacing) * gen/2       */
 72  
 73          /* Next, compute the table entries for block number block in Jacobian coordinates.
 74           * The entries will occupy vs[block*points + i] for i=0..points-1.
 75           * We start by computing the first (i=0) value corresponding to all summed
 76           * powers of two times G being negative. */
 77          secp256k1_gej_neg(&vs[vs_pos++], &sum);
 78          /* And then teeth-1 times "double" the range of i values for which the table
 79           * is computed: in each iteration, double the table by taking an existing
 80           * table entry and adding ds[tooth]. */
 81          for (tooth = 0; tooth < teeth - 1; ++tooth) {
 82              size_t stride = ((size_t)1) << tooth;
 83              size_t index;
 84              for (index = 0; index < stride; ++index, ++vs_pos) {
 85                  secp256k1_gej_add_var(&vs[vs_pos], &vs[vs_pos - stride], &ds[tooth], NULL);
 86              }
 87          }
 88      }
 89      VERIFY_CHECK(vs_pos == points_total);
 90  
 91      /* Convert all points simultaneously from secp256k1_gej to secp256k1_ge. */
 92      secp256k1_ge_set_all_gej_var(prec, vs, points_total);
 93      /* Convert all points from secp256k1_ge to secp256k1_ge_storage output. */
 94      for (block = 0; block < blocks; ++block) {
 95          size_t index;
 96          for (index = 0; index < points; ++index) {
 97              VERIFY_CHECK(!secp256k1_ge_is_infinity(&prec[block * points + index]));
 98              secp256k1_ge_to_storage(&table[block * points + index], &prec[block * points + index]);
 99          }
100      }
101  
102      /* Free memory. */
103      free(vs);
104      free(ds);
105      free(prec);
106  }
107  
108  #endif /* SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H */