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crypto: Add Num3072 implementation
Num3072 is a specialized bignum implementation used in MuHash3072. Co-authored-by: Pieter Wuille <pieter.wuille@gmail.com>
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Fabian Jahr
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277
src/crypto/muhash.cpp
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277
src/crypto/muhash.cpp
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// Copyright (c) 2017-2020 The Bitcoin Core developers
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// Distributed under the MIT software license, see the accompanying
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// file COPYING or http://www.opensource.org/licenses/mit-license.php.
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#include <crypto/muhash.h>
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#include <crypto/chacha20.h>
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#include <crypto/common.h>
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#include <hash.h>
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#include <cassert>
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#include <cstdio>
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#include <limits>
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namespace {
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using limb_t = Num3072::limb_t;
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using double_limb_t = Num3072::double_limb_t;
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constexpr int LIMB_SIZE = Num3072::LIMB_SIZE;
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constexpr int LIMBS = Num3072::LIMBS;
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/** 2^3072 - 1103717, the largest 3072-bit safe prime number, is used as the modulus. */
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constexpr limb_t MAX_PRIME_DIFF = 1103717;
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/** Extract the lowest limb of [c0,c1,c2] into n, and left shift the number by 1 limb. */
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inline void extract3(limb_t& c0, limb_t& c1, limb_t& c2, limb_t& n)
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{
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n = c0;
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c0 = c1;
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c1 = c2;
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c2 = 0;
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}
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/** [c0,c1] = a * b */
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inline void mul(limb_t& c0, limb_t& c1, const limb_t& a, const limb_t& b)
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{
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double_limb_t t = (double_limb_t)a * b;
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c1 = t >> LIMB_SIZE;
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c0 = t;
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}
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/* [c0,c1,c2] += n * [d0,d1,d2]. c2 is 0 initially */
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inline void mulnadd3(limb_t& c0, limb_t& c1, limb_t& c2, limb_t& d0, limb_t& d1, limb_t& d2, const limb_t& n)
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{
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double_limb_t t = (double_limb_t)d0 * n + c0;
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c0 = t;
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t >>= LIMB_SIZE;
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t += (double_limb_t)d1 * n + c1;
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c1 = t;
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t >>= LIMB_SIZE;
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c2 = t + d2 * n;
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}
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/* [c0,c1] *= n */
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inline void muln2(limb_t& c0, limb_t& c1, const limb_t& n)
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{
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double_limb_t t = (double_limb_t)c0 * n;
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c0 = t;
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t >>= LIMB_SIZE;
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t += (double_limb_t)c1 * n;
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c1 = t;
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}
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/** [c0,c1,c2] += a * b */
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inline void muladd3(limb_t& c0, limb_t& c1, limb_t& c2, const limb_t& a, const limb_t& b)
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{
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double_limb_t t = (double_limb_t)a * b;
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limb_t th = t >> LIMB_SIZE;
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limb_t tl = t;
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c0 += tl;
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th += (c0 < tl) ? 1 : 0;
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c1 += th;
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c2 += (c1 < th) ? 1 : 0;
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}
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/** [c0,c1,c2] += 2 * a * b */
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inline void muldbladd3(limb_t& c0, limb_t& c1, limb_t& c2, const limb_t& a, const limb_t& b)
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{
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double_limb_t t = (double_limb_t)a * b;
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limb_t th = t >> LIMB_SIZE;
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limb_t tl = t;
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c0 += tl;
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limb_t tt = th + ((c0 < tl) ? 1 : 0);
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c1 += tt;
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c2 += (c1 < tt) ? 1 : 0;
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c0 += tl;
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th += (c0 < tl) ? 1 : 0;
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c1 += th;
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c2 += (c1 < th) ? 1 : 0;
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}
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/**
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* Add limb a to [c0,c1]: [c0,c1] += a. Then extract the lowest
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* limb of [c0,c1] into n, and left shift the number by 1 limb.
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* */
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inline void addnextract2(limb_t& c0, limb_t& c1, const limb_t& a, limb_t& n)
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{
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limb_t c2 = 0;
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// add
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c0 += a;
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if (c0 < a) {
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c1 += 1;
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// Handle case when c1 has overflown
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if (c1 == 0)
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c2 = 1;
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}
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// extract
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n = c0;
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c0 = c1;
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c1 = c2;
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}
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/** in_out = in_out^(2^sq) * mul */
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inline void square_n_mul(Num3072& in_out, const int sq, const Num3072& mul)
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{
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for (int j = 0; j < sq; ++j) in_out.Square();
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in_out.Multiply(mul);
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}
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} // namespace
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/** Indicates wether d is larger than the modulus. */
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bool Num3072::IsOverflow() const
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{
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if (this->limbs[0] <= std::numeric_limits<limb_t>::max() - MAX_PRIME_DIFF) return false;
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for (int i = 1; i < LIMBS; ++i) {
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if (this->limbs[i] != std::numeric_limits<limb_t>::max()) return false;
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}
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return true;
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}
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void Num3072::FullReduce()
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{
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limb_t c0 = MAX_PRIME_DIFF;
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limb_t c1 = 0;
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for (int i = 0; i < LIMBS; ++i) {
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addnextract2(c0, c1, this->limbs[i], this->limbs[i]);
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}
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}
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Num3072 Num3072::GetInverse() const
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{
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// For fast exponentiation a sliding window exponentiation with repunit
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// precomputation is utilized. See "Fast Point Decompression for Standard
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// Elliptic Curves" (Brumley, Järvinen, 2008).
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Num3072 p[12]; // p[i] = a^(2^(2^i)-1)
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Num3072 out;
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p[0] = *this;
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for (int i = 0; i < 11; ++i) {
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p[i + 1] = p[i];
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for (int j = 0; j < (1 << i); ++j) p[i + 1].Square();
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p[i + 1].Multiply(p[i]);
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}
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out = p[11];
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square_n_mul(out, 512, p[9]);
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square_n_mul(out, 256, p[8]);
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square_n_mul(out, 128, p[7]);
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square_n_mul(out, 64, p[6]);
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square_n_mul(out, 32, p[5]);
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square_n_mul(out, 8, p[3]);
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square_n_mul(out, 2, p[1]);
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square_n_mul(out, 1, p[0]);
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square_n_mul(out, 5, p[2]);
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square_n_mul(out, 3, p[0]);
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square_n_mul(out, 2, p[0]);
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square_n_mul(out, 4, p[0]);
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square_n_mul(out, 4, p[1]);
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square_n_mul(out, 3, p[0]);
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return out;
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}
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void Num3072::Multiply(const Num3072& a)
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{
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limb_t c0 = 0, c1 = 0, c2 = 0;
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Num3072 tmp;
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/* Compute limbs 0..N-2 of this*a into tmp, including one reduction. */
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for (int j = 0; j < LIMBS - 1; ++j) {
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limb_t d0 = 0, d1 = 0, d2 = 0;
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mul(d0, d1, this->limbs[1 + j], a.limbs[LIMBS + j - (1 + j)]);
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for (int i = 2 + j; i < LIMBS; ++i) muladd3(d0, d1, d2, this->limbs[i], a.limbs[LIMBS + j - i]);
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mulnadd3(c0, c1, c2, d0, d1, d2, MAX_PRIME_DIFF);
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for (int i = 0; i < j + 1; ++i) muladd3(c0, c1, c2, this->limbs[i], a.limbs[j - i]);
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extract3(c0, c1, c2, tmp.limbs[j]);
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}
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/* Compute limb N-1 of a*b into tmp. */
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assert(c2 == 0);
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for (int i = 0; i < LIMBS; ++i) muladd3(c0, c1, c2, this->limbs[i], a.limbs[LIMBS - 1 - i]);
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extract3(c0, c1, c2, tmp.limbs[LIMBS - 1]);
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/* Perform a second reduction. */
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muln2(c0, c1, MAX_PRIME_DIFF);
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for (int j = 0; j < LIMBS; ++j) {
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addnextract2(c0, c1, tmp.limbs[j], this->limbs[j]);
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}
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assert(c1 == 0);
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assert(c0 == 0 || c0 == 1);
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/* Perform up to two more reductions if the internal state has already
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* overflown the MAX of Num3072 or if it is larger than the modulus or
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* if both are the case.
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* */
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if (this->IsOverflow()) this->FullReduce();
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if (c0) this->FullReduce();
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}
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void Num3072::Square()
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{
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limb_t c0 = 0, c1 = 0, c2 = 0;
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Num3072 tmp;
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/* Compute limbs 0..N-2 of this*this into tmp, including one reduction. */
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for (int j = 0; j < LIMBS - 1; ++j) {
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limb_t d0 = 0, d1 = 0, d2 = 0;
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for (int i = 0; i < (LIMBS - 1 - j) / 2; ++i) muldbladd3(d0, d1, d2, this->limbs[i + j + 1], this->limbs[LIMBS - 1 - i]);
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if ((j + 1) & 1) muladd3(d0, d1, d2, this->limbs[(LIMBS - 1 - j) / 2 + j + 1], this->limbs[LIMBS - 1 - (LIMBS - 1 - j) / 2]);
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mulnadd3(c0, c1, c2, d0, d1, d2, MAX_PRIME_DIFF);
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for (int i = 0; i < (j + 1) / 2; ++i) muldbladd3(c0, c1, c2, this->limbs[i], this->limbs[j - i]);
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if ((j + 1) & 1) muladd3(c0, c1, c2, this->limbs[(j + 1) / 2], this->limbs[j - (j + 1) / 2]);
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extract3(c0, c1, c2, tmp.limbs[j]);
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}
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assert(c2 == 0);
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for (int i = 0; i < LIMBS / 2; ++i) muldbladd3(c0, c1, c2, this->limbs[i], this->limbs[LIMBS - 1 - i]);
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extract3(c0, c1, c2, tmp.limbs[LIMBS - 1]);
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/* Perform a second reduction. */
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muln2(c0, c1, MAX_PRIME_DIFF);
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for (int j = 0; j < LIMBS; ++j) {
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addnextract2(c0, c1, tmp.limbs[j], this->limbs[j]);
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}
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assert(c1 == 0);
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assert(c0 == 0 || c0 == 1);
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/* Perform up to two more reductions if the internal state has already
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* overflown the MAX of Num3072 or if it is larger than the modulus or
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* if both are the case.
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* */
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if (this->IsOverflow()) this->FullReduce();
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if (c0) this->FullReduce();
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}
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void Num3072::SetToOne()
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{
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this->limbs[0] = 1;
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for (int i = 1; i < LIMBS; ++i) this->limbs[i] = 0;
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}
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void Num3072::Divide(const Num3072& a)
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{
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if (this->IsOverflow()) this->FullReduce();
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Num3072 inv{};
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if (a.IsOverflow()) {
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Num3072 b = a;
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b.FullReduce();
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inv = b.GetInverse();
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} else {
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inv = a.GetInverse();
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}
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this->Multiply(inv);
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if (this->IsOverflow()) this->FullReduce();
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}
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62
src/crypto/muhash.h
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62
src/crypto/muhash.h
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// Copyright (c) 2017-2020 The Bitcoin Core developers
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// Distributed under the MIT software license, see the accompanying
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// file COPYING or http://www.opensource.org/licenses/mit-license.php.
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#ifndef BITCOIN_CRYPTO_MUHASH_H
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#define BITCOIN_CRYPTO_MUHASH_H
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#if defined(HAVE_CONFIG_H)
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#include <config/bitcoin-config.h>
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#endif
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#include <serialize.h>
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#include <uint256.h>
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#include <stdint.h>
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class Num3072
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{
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private:
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void FullReduce();
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bool IsOverflow() const;
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Num3072 GetInverse() const;
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public:
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#ifdef HAVE___INT128
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typedef unsigned __int128 double_limb_t;
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typedef uint64_t limb_t;
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static constexpr int LIMBS = 48;
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static constexpr int LIMB_SIZE = 64;
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#else
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typedef uint64_t double_limb_t;
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typedef uint32_t limb_t;
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static constexpr int LIMBS = 96;
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static constexpr int LIMB_SIZE = 32;
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#endif
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limb_t limbs[LIMBS];
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// Sanity check for Num3072 constants
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static_assert(LIMB_SIZE * LIMBS == 3072, "Num3072 isn't 3072 bits");
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static_assert(sizeof(double_limb_t) == sizeof(limb_t) * 2, "bad size for double_limb_t");
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static_assert(sizeof(limb_t) * 8 == LIMB_SIZE, "LIMB_SIZE is incorrect");
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// Hard coded values in MuHash3072 constructor and Finalize
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static_assert(sizeof(limb_t) == 4 || sizeof(limb_t) == 8, "bad size for limb_t");
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void Multiply(const Num3072& a);
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void Divide(const Num3072& a);
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void SetToOne();
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void Square();
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Num3072() { this->SetToOne(); };
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SERIALIZE_METHODS(Num3072, obj)
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{
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for (auto& limb : obj.limbs) {
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READWRITE(limb);
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}
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}
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};
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#endif // BITCOIN_CRYPTO_MUHASH_H
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