muhash.cpp

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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 limb_t MAX_PRIME_DIFF = 1103717;
 
inline void extract3(limb_t &c0, limb_t &c1, limb_t &c2, limb_t &n) {
    n = c0;
    c0 = c1;
    c1 = c2;
    c2 = 0;
}
 
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;
}
 
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;
}
 
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;
}
 
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;
}
 
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
 
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).
 
    // p[i] = a^(2^(2^i)-1)
    Num3072 p[12];
 
    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]);
    }
 
    Num3072 out;
 
    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);
 
    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);
 
    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();
    }
}
 
Num3072::Num3072(const uint8_t (&data)[BYTE_SIZE]) {
    for (int i = 0; i < LIMBS; ++i) {
        if (sizeof(limb_t) == 4) {
            this->limbs[i] = ReadLE32(data + 4 * i);
        } else if (sizeof(limb_t) == 8) {
            this->limbs[i] = ReadLE64(data + 8 * i);
        }
    }
}
 
void Num3072::ToBytes(uint8_t (&out)[BYTE_SIZE]) {
    for (int i = 0; i < LIMBS; ++i) {
        if (sizeof(limb_t) == 4) {
            WriteLE32(out + i * 4, this->limbs[i]);
        } else if (sizeof(limb_t) == 8) {
            WriteLE64(out + i * 8, this->limbs[i]);
        }
    }
}
 
Num3072 MuHash3072::ToNum3072(Span<const uint8_t> in) {
    uint8_t tmp[Num3072::BYTE_SIZE];
 
    uint256 hashed_in{(HashWriter{} << in).GetSHA256()};
    ChaCha20(hashed_in.data(), hashed_in.size())
        .Keystream(tmp, Num3072::BYTE_SIZE);
    Num3072 out{tmp};
 
    return out;
}
 
MuHash3072::MuHash3072(Span<const uint8_t> in) noexcept {
    m_numerator = ToNum3072(in);
}
 
void MuHash3072::Finalize(uint256 &out) noexcept {
    m_numerator.Divide(m_denominator);
    // Needed to keep the MuHash object valid
    m_denominator.SetToOne();
 
    uint8_t data[Num3072::BYTE_SIZE];
    m_numerator.ToBytes(data);
 
    out = (HashWriter{} << data).GetSHA256();
}
 
MuHash3072 &MuHash3072::operator*=(const MuHash3072 &mul) noexcept {
    m_numerator.Multiply(mul.m_numerator);
    m_denominator.Multiply(mul.m_denominator);
    return *this;
}
 
MuHash3072 &MuHash3072::operator/=(const MuHash3072 &div) noexcept {
    m_numerator.Multiply(div.m_denominator);
    m_denominator.Multiply(div.m_numerator);
    return *this;
}
 
MuHash3072 &MuHash3072::Insert(Span<const uint8_t> in) noexcept {
    m_numerator.Multiply(ToNum3072(in));
    return *this;
}
 
MuHash3072 &MuHash3072::Remove(Span<const uint8_t> in) noexcept {
    m_denominator.Multiply(ToNum3072(in));
    return *this;
}