bitcoin/src/ecmult_gen_impl.h

// Copyright (c) 2013-2014 Pieter Wuille
// Distributed under the MIT software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.

#ifndef _SECP256K1_ECMULT_GEN_IMPL_H_
#define _SECP256K1_ECMULT_GEN_IMPL_H_

#include <assert.h>
#include "scalar.h"
#include "group.h"
#include "ecmult_gen.h"

typedef struct {
    // For accelerating the computation of a*G:
    // To harden against timing attacks, use the following mechanism:
    // * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
    // * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
    //   * U_i = U * 2^i (for i=0..62)
    //   * U_i = U * (1-2^63) (for i=63)
    //   where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
    // For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
    // precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
    // None of the resulting prec group elements have a known scalar, and neither do any of
    // the intermediate sums while computing a*G.
    // To make memory access uniform, the bytes of prec(i, n_i) are sliced per value of n_i.
    unsigned char prec[64][sizeof(secp256k1_ge_t)][16]; // prec[j][k][i] = k'th byte of (16^j * i * G + U_i)
} secp256k1_ecmult_gen_consts_t;

static const secp256k1_ecmult_gen_consts_t *secp256k1_ecmult_gen_consts = NULL;

static void secp256k1_ecmult_gen_start(void) {
    if (secp256k1_ecmult_gen_consts != NULL)
        return;

    // Allocate the precomputation table.
    secp256k1_ecmult_gen_consts_t *ret = (secp256k1_ecmult_gen_consts_t*)malloc(sizeof(secp256k1_ecmult_gen_consts_t));

    // get the generator
    const secp256k1_ge_t *g = &secp256k1_ge_consts->g;
    secp256k1_gej_t gj; secp256k1_gej_set_ge(&gj, g);

    // Construct a group element with no known corresponding scalar (nothing up my sleeve).
    secp256k1_gej_t nums_gej;
    {
        static const unsigned char nums_b32[32] = "The scalar for this x is unknown";
        secp256k1_fe_t nums_x;
        secp256k1_fe_set_b32(&nums_x, nums_b32);
        secp256k1_ge_t nums_ge;
        VERIFY_CHECK(secp256k1_ge_set_xo(&nums_ge, &nums_x, 0));
        secp256k1_gej_set_ge(&nums_gej, &nums_ge);
        // Add G to make the bits in x uniformly distributed.
        secp256k1_gej_add_ge(&nums_gej, &nums_gej, g);
    }

    // compute prec.
    secp256k1_ge_t prec[1024];
    {
        secp256k1_gej_t precj[1024]; // Jacobian versions of prec.
        int j = 0;
        secp256k1_gej_t gbase; gbase = gj; // 16^j * G
        secp256k1_gej_t numsbase; numsbase = nums_gej; // 2^j * nums.
        for (int j=0; j<64; j++) {
            // Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase).
            precj[j*16] = numsbase;
            for (int i=1; i<16; i++) {
                secp256k1_gej_add(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase);
            }
            // Multiply gbase by 16.
            for (int i=0; i<4; i++) {
                secp256k1_gej_double(&gbase, &gbase);
            }
            // Multiply numbase by 2.
            secp256k1_gej_double(&numsbase, &numsbase);
            if (j == 62) {
                // In the last iteration, numsbase is (1 - 2^j) * nums instead.
                secp256k1_gej_neg(&numsbase, &numsbase);
                secp256k1_gej_add(&numsbase, &numsbase, &nums_gej);
            }
        }
        secp256k1_ge_set_all_gej(1024, prec, precj);
    }
    for (int j=0; j<64; j++) {
        for (int i=0; i<16; i++) {
            const unsigned char* raw = (const unsigned char*)(&prec[j*16 + i]);
            for (int k=0; k<sizeof(secp256k1_ge_t); k++)
                ret->prec[j][k][i] = raw[k];
        }
    }

    // Set the global pointer to the precomputation table.
    secp256k1_ecmult_gen_consts = ret;
}

static void secp256k1_ecmult_gen_stop(void) {
    if (secp256k1_ecmult_gen_consts == NULL)
        return;

    secp256k1_ecmult_gen_consts_t *c = (secp256k1_ecmult_gen_consts_t*)secp256k1_ecmult_gen_consts;
    secp256k1_ecmult_gen_consts = NULL;
    free(c);
}

void static secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_scalar_t *gn) {
    const secp256k1_ecmult_gen_consts_t *c = secp256k1_ecmult_gen_consts;
    secp256k1_gej_set_infinity(r);
    secp256k1_ge_t add;
    int bits;
    for (int j=0; j<64; j++) {
        bits = secp256k1_scalar_get_bits(gn, j * 4, 4);
        for (int k=0; k<sizeof(secp256k1_ge_t); k++)
            ((unsigned char*)(&add))[k] = c->prec[j][k][bits];
        secp256k1_gej_add_ge(r, r, &add);
    }
    bits = 0;
    secp256k1_ge_clear(&add);
}

#endif