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// Copyright (c) 2017-2020 The Bitcoin Core developers
// Distributed under the MIT software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#include <crypto/muhash.h>
#include <crypto/chacha20.h>
#include <crypto/common.h>
#include <hash.h>
#include <cassert>
#include <cstdio>
#include <limits>
namespace {
using limb_t = Num3072::limb_t;
using double_limb_t = Num3072::double_limb_t;
constexpr int LIMB_SIZE = Num3072::LIMB_SIZE;
constexpr int LIMBS = Num3072::LIMBS;
/** 2^3072 - 1103717, the largest 3072-bit safe prime number, is used as the modulus. */
constexpr limb_t MAX_PRIME_DIFF = 1103717;
/** Extract the lowest limb of [c0,c1,c2] into n, and left shift the number by 1 limb. */
inline void extract3(limb_t& c0, limb_t& c1, limb_t& c2, limb_t& n)
{
n = c0;
c0 = c1;
c1 = c2;
c2 = 0;
}
/** [c0,c1] = a * b */
inline void mul(limb_t& c0, limb_t& c1, const limb_t& a, const limb_t& b)
{
double_limb_t t = (double_limb_t)a * b;
c1 = t >> LIMB_SIZE;
c0 = t;
}
/* [c0,c1,c2] += n * [d0,d1,d2]. c2 is 0 initially */
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)
{
double_limb_t t = (double_limb_t)d0 * n + c0;
c0 = t;
t >>= LIMB_SIZE;
t += (double_limb_t)d1 * n + c1;
c1 = t;
t >>= LIMB_SIZE;
c2 = t + d2 * n;
}
/* [c0,c1] *= n */
inline void muln2(limb_t& c0, limb_t& c1, const limb_t& n)
{
double_limb_t t = (double_limb_t)c0 * n;
c0 = t;
t >>= LIMB_SIZE;
t += (double_limb_t)c1 * n;
c1 = t;
}
/** [c0,c1,c2] += a * b */
inline void muladd3(limb_t& c0, limb_t& c1, limb_t& c2, const limb_t& a, const limb_t& b)
{
double_limb_t t = (double_limb_t)a * b;
limb_t th = t >> LIMB_SIZE;
limb_t tl = t;
c0 += tl;
th += (c0 < tl) ? 1 : 0;
c1 += th;
c2 += (c1 < th) ? 1 : 0;
}
/** [c0,c1,c2] += 2 * a * b */
inline void muldbladd3(limb_t& c0, limb_t& c1, limb_t& c2, const limb_t& a, const limb_t& b)
{
double_limb_t t = (double_limb_t)a * b;
limb_t th = t >> LIMB_SIZE;
limb_t tl = t;
c0 += tl;
limb_t tt = th + ((c0 < tl) ? 1 : 0);
c1 += tt;
c2 += (c1 < tt) ? 1 : 0;
c0 += tl;
th += (c0 < tl) ? 1 : 0;
c1 += th;
c2 += (c1 < th) ? 1 : 0;
}
/**
* Add limb a to [c0,c1]: [c0,c1] += a. Then extract the lowest
* limb of [c0,c1] into n, and left shift the number by 1 limb.
* */
inline void addnextract2(limb_t& c0, limb_t& c1, const limb_t& a, limb_t& n)
{
limb_t c2 = 0;
// add
c0 += a;
if (c0 < a) {
c1 += 1;
// Handle case when c1 has overflown
if (c1 == 0)
c2 = 1;
}
// extract
n = c0;
c0 = c1;
c1 = c2;
}
/** in_out = in_out^(2^sq) * mul */
inline void square_n_mul(Num3072& in_out, const int sq, const Num3072& mul)
{
for (int j = 0; j < sq; ++j) in_out.Square();
in_out.Multiply(mul);
}
} // namespace
/** Indicates wether d is larger than the modulus. */
bool Num3072::IsOverflow() const
{
if (this->limbs[0] <= std::numeric_limits<limb_t>::max() - MAX_PRIME_DIFF) return false;
for (int i = 1; i < LIMBS; ++i) {
if (this->limbs[i] != std::numeric_limits<limb_t>::max()) return false;
}
return true;
}
void Num3072::FullReduce()
{
limb_t c0 = MAX_PRIME_DIFF;
limb_t c1 = 0;
for (int i = 0; i < LIMBS; ++i) {
addnextract2(c0, c1, this->limbs[i], this->limbs[i]);
}
}
Num3072 Num3072::GetInverse() const
{
// For fast exponentiation a sliding window exponentiation with repunit
// precomputation is utilized. See "Fast Point Decompression for Standard
// Elliptic Curves" (Brumley, Järvinen, 2008).
Num3072 p[12]; // p[i] = a^(2^(2^i)-1)
Num3072 out;
p[0] = *this;
for (int i = 0; i < 11; ++i) {
p[i + 1] = p[i];
for (int j = 0; j < (1 << i); ++j) p[i + 1].Square();
p[i + 1].Multiply(p[i]);
}
out = p[11];
square_n_mul(out, 512, p[9]);
square_n_mul(out, 256, p[8]);
square_n_mul(out, 128, p[7]);
square_n_mul(out, 64, p[6]);
square_n_mul(out, 32, p[5]);
square_n_mul(out, 8, p[3]);
square_n_mul(out, 2, p[1]);
square_n_mul(out, 1, p[0]);
square_n_mul(out, 5, p[2]);
square_n_mul(out, 3, p[0]);
square_n_mul(out, 2, p[0]);
square_n_mul(out, 4, p[0]);
square_n_mul(out, 4, p[1]);
square_n_mul(out, 3, p[0]);
return out;
}
void Num3072::Multiply(const Num3072& a)
{
limb_t c0 = 0, c1 = 0, c2 = 0;
Num3072 tmp;
/* Compute limbs 0..N-2 of this*a into tmp, including one reduction. */
for (int j = 0; j < LIMBS - 1; ++j) {
limb_t d0 = 0, d1 = 0, d2 = 0;
mul(d0, d1, this->limbs[1 + j], a.limbs[LIMBS + j - (1 + j)]);
for (int i = 2 + j; i < LIMBS; ++i) muladd3(d0, d1, d2, this->limbs[i], a.limbs[LIMBS + j - i]);
mulnadd3(c0, c1, c2, d0, d1, d2, MAX_PRIME_DIFF);
for (int i = 0; i < j + 1; ++i) muladd3(c0, c1, c2, this->limbs[i], a.limbs[j - i]);
extract3(c0, c1, c2, tmp.limbs[j]);
}
/* Compute limb N-1 of a*b into tmp. */
assert(c2 == 0);
for (int i = 0; i < LIMBS; ++i) muladd3(c0, c1, c2, this->limbs[i], a.limbs[LIMBS - 1 - i]);
extract3(c0, c1, c2, tmp.limbs[LIMBS - 1]);
/* Perform a second reduction. */
muln2(c0, c1, MAX_PRIME_DIFF);
for (int j = 0; j < LIMBS; ++j) {
addnextract2(c0, c1, tmp.limbs[j], this->limbs[j]);
}
assert(c1 == 0);
assert(c0 == 0 || c0 == 1);
/* Perform up to two more reductions if the internal state has already
* overflown the MAX of Num3072 or if it is larger than the modulus or
* if both are the case.
* */
if (this->IsOverflow()) this->FullReduce();
if (c0) this->FullReduce();
}
void Num3072::Square()
{
limb_t c0 = 0, c1 = 0, c2 = 0;
Num3072 tmp;
/* Compute limbs 0..N-2 of this*this into tmp, including one reduction. */
for (int j = 0; j < LIMBS - 1; ++j) {
limb_t d0 = 0, d1 = 0, d2 = 0;
for (int i = 0; i < (LIMBS - 1 - j) / 2; ++i) muldbladd3(d0, d1, d2, this->limbs[i + j + 1], this->limbs[LIMBS - 1 - i]);
if ((j + 1) & 1) muladd3(d0, d1, d2, this->limbs[(LIMBS - 1 - j) / 2 + j + 1], this->limbs[LIMBS - 1 - (LIMBS - 1 - j) / 2]);
mulnadd3(c0, c1, c2, d0, d1, d2, MAX_PRIME_DIFF);
for (int i = 0; i < (j + 1) / 2; ++i) muldbladd3(c0, c1, c2, this->limbs[i], this->limbs[j - i]);
if ((j + 1) & 1) muladd3(c0, c1, c2, this->limbs[(j + 1) / 2], this->limbs[j - (j + 1) / 2]);
extract3(c0, c1, c2, tmp.limbs[j]);
}
assert(c2 == 0);
for (int i = 0; i < LIMBS / 2; ++i) muldbladd3(c0, c1, c2, this->limbs[i], this->limbs[LIMBS - 1 - i]);
extract3(c0, c1, c2, tmp.limbs[LIMBS - 1]);
/* Perform a second reduction. */
muln2(c0, c1, MAX_PRIME_DIFF);
for (int j = 0; j < LIMBS; ++j) {
addnextract2(c0, c1, tmp.limbs[j], this->limbs[j]);
}
assert(c1 == 0);
assert(c0 == 0 || c0 == 1);
/* Perform up to two more reductions if the internal state has already
* overflown the MAX of Num3072 or if it is larger than the modulus or
* if both are the case.
* */
if (this->IsOverflow()) this->FullReduce();
if (c0) this->FullReduce();
}
void Num3072::SetToOne()
{
this->limbs[0] = 1;
for (int i = 1; i < LIMBS; ++i) this->limbs[i] = 0;
}
void Num3072::Divide(const Num3072& a)
{
if (this->IsOverflow()) this->FullReduce();
Num3072 inv{};
if (a.IsOverflow()) {
Num3072 b = a;
b.FullReduce();
inv = b.GetInverse();
} else {
inv = a.GetInverse();
}
this->Multiply(inv);
if (this->IsOverflow()) this->FullReduce();
}
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