monero/src/crypto/generators.cpp

// Copyright (c) 2022-2026, The Monero Project
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#include "generators.h"

#include "crypto.h"
extern "C"
{
#include "crypto-ops.h"
}
#include "hash.h"

#include <cassert>
#include <mutex>
#include <string_view>

namespace crypto
{

/// constexpr assert for old gcc bug: https://stackoverflow.com/questions/34280729/throw-in-constexpr-function
/// - this function won't compile in a constexpr context if b == false
constexpr void constexpr_assert(const bool b) { b ? 0 : throw std::runtime_error("constexpr assert failed"); };

/// constexpr paste bytes into an array-of-bytes type
template<typename T>
constexpr T bytes_to(const std::initializer_list<unsigned char> bytes)
{
    T out{}; // zero-initialize trailing bytes

    auto current = std::begin(out.data);
    constexpr_assert(static_cast<long>(bytes.size()) <= std::end(out.data) - current);

    for (const unsigned char byte : bytes)
        *current++ = byte;
    return out;
}

// generators
//standard ed25519 generator G: {x, 4/5} (positive x when decompressing y = 4/5)
constexpr public_key G = bytes_to<public_key>({ 0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
    0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66 });
//pedersen commitment generator H: toPoint(cn_fast_hash(G))
constexpr public_key H = bytes_to<public_key>({ 0x8b, 0x65, 0x59, 0x70, 0x15, 0x37, 0x99, 0xaf, 0x2a, 0xea, 0xdc, 0x9f, 0xf1,
    0xad, 0xd0, 0xea, 0x6c, 0x72, 0x51, 0xd5, 0x41, 0x54, 0xcf, 0xa9, 0x2c, 0x17, 0x3a, 0x0d, 0xd3, 0x9c, 0x1f, 0x94 });
//FCMP++ generator T: unbiased_hash_to_ec(Keccak256("Monero Generator T"))
//Source: https://github.com/monero-oxide/monero-oxide/blob/0e438aed2cce5c0ab8a935916c1a89bb0077f97f/monero-oxide/ed25519/src/compressed_point.rs#L76-L79
constexpr public_key T = bytes_to<public_key>({ 97, 183, 54, 206, 147, 182, 42, 61, 55, 120, 171, 32, 77, 168, 93, 59, 76,
  220, 7, 37, 15, 93, 167, 227, 223, 38, 41, 146, 129, 52, 213, 38 });
//FCMP++ generator U: unbiased_hash_to_ec(Keccak256("Monero FCMP++ Generator U"))
//Source: https://github.com/monero-oxide/monero-oxide/blob/0e438aed2cce5c0ab8a935916c1a89bb0077f97f/monero-oxide/ringct/fcmp%2B%2B/generators/src/lib.rs#L16-L18
constexpr public_key U = bytes_to<public_key>({ 80, 107, 35, 246, 214, 229, 48, 153, 122, 188, 172, 198, 253, 52, 119, 52,
  177, 76, 43, 215, 155, 234, 0, 238, 176, 72, 87, 232, 234, 221, 26, 138 });
//FCMP++ generator V: unbiased_hash_to_ec(Keccak256("Monero FCMP++ Generator V"))
//Source: https://github.com/monero-oxide/monero-oxide/blob/0e438aed2cce5c0ab8a935916c1a89bb0077f97f/monero-oxide/ringct/fcmp%2B%2B/generators/src/lib.rs#L20-L22
constexpr public_key V = bytes_to<public_key>({ 105, 53, 244, 19, 248, 49, 9, 19, 138, 122, 20, 180, 9, 85, 45, 59, 118,
  216, 143, 202, 129, 187, 89, 39, 233, 161, 225, 48, 205, 254, 41, 249 });
static ge_p3 G_p3;
static ge_p3 H_p3;
static ge_p3 T_p3;
static ge_p3 U_p3;
static ge_p3 V_p3;
static ge_cached G_cached;
static ge_cached H_cached;
static ge_cached T_cached;
static ge_cached U_cached;
static ge_cached V_cached;

// misc
static std::once_flag init_gens_once_flag;

//-------------------------------------------------------------------------------------------------------------------
//-------------------------------------------------------------------------------------------------------------------
/**
 * @brief P = H^2_p(Keccak256(seed)) = Elligator2(Blake2b_512[personal="Monero"](Keccak256(seed)))
 * @param seed arbitrary seed string for generator
 * @param[out] point_out P
 * @see `unbiased_hash_to_ec()`
 */
static void unbiased_hash_to_hash_to_ec(const std::string_view seed, crypto::ec_point &point_out)
{
    const crypto::hash seed_hash = cn_fast_hash(seed.data(), seed.size());
    unbiased_hash_to_ec(reinterpret_cast<const unsigned char*>(&seed_hash), sizeof(crypto::hash), point_out);
}
//-------------------------------------------------------------------------------------------------------------------
//-------------------------------------------------------------------------------------------------------------------
static public_key reproduce_generator_G()
{
    // G = {x, 4/5 mod q}
    fe four, five, inv_five, y;
    fe_0(four);
    fe_0(five);
    four[0] = 4;
    five[0] = 5;
    fe_invert(inv_five, five);
    fe_mul(y, four, inv_five);

    public_key reproduced_G;
    fe_tobytes(to_bytes(reproduced_G), y);

    return reproduced_G;
}
//-------------------------------------------------------------------------------------------------------------------
//-------------------------------------------------------------------------------------------------------------------
static public_key reproduce_generator_H()
{
    // H = 8*to_point(keccak(G))
    // note: this does not use the point_from_bytes() function found in H_p(), instead directly interpreting the
    //       input bytes as a compressed point (this can fail, so should not be used generically)
    // note2: to_point(keccak(G)) is known to succeed for the canonical value of G (it will fail 7/8ths of the time
    //        normally)
    ge_p3 temp_p3;
    ge_p2 temp_p2;
    ge_p1p1 temp_p1p1;

    hash H_temp_hash{cn_fast_hash(to_bytes(G), sizeof(ec_point))};
    (void)H_temp_hash;  //suppress unused warning
    assert(ge_frombytes_vartime(&temp_p3, reinterpret_cast<const unsigned char*>(&H_temp_hash)) == 0);
    ge_p3_to_p2(&temp_p2, &temp_p3);
    ge_mul8(&temp_p1p1, &temp_p2);
    ge_p1p1_to_p3(&temp_p3, &temp_p1p1);

    public_key reproduced_H;
    ge_p3_tobytes(to_bytes(reproduced_H), &temp_p3);

    return reproduced_H;
}
//-------------------------------------------------------------------------------------------------------------------
//-------------------------------------------------------------------------------------------------------------------
static public_key reproduce_generator_T()
{
    // T = unbiased_hash_to_hash_to_ec("Monero Generator T"))
    //   = Elligator2(Blake2b_512[personal="Monero"](Keccak256("Monero Generator T")))
    const std::string_view T_seed{"Monero Generator T"};
    public_key reproduced_T;
    unbiased_hash_to_hash_to_ec(T_seed, reproduced_T);
    return reproduced_T;
}
//-------------------------------------------------------------------------------------------------------------------
//-------------------------------------------------------------------------------------------------------------------
static public_key reproduce_generator_U()
{
    // U = unbiased_hash_to_hash_to_ec("Monero FCMP++ Generator U"))
    //   = Elligator2(Blake2b_512[personal="Monero"](Keccak256("Monero FCMP++ Generator U")))
    const std::string_view U_seed{"Monero FCMP++ Generator U"};
    public_key reproduced_U;
    unbiased_hash_to_hash_to_ec(U_seed, reproduced_U);
    return reproduced_U;
}
//-------------------------------------------------------------------------------------------------------------------
//-------------------------------------------------------------------------------------------------------------------
static public_key reproduce_generator_V()
{
    // V = unbiased_hash_to_hash_to_ec("Monero FCMP++ Generator V"))
    //   = Elligator2(Blake2b_512[personal="Monero"](Keccak256("Monero FCMP++ Generator V")))
    const std::string_view V_seed{"Monero FCMP++ Generator V"};
    public_key reproduced_V;
    unbiased_hash_to_hash_to_ec(V_seed, reproduced_V);
    return reproduced_V;
}
//-------------------------------------------------------------------------------------------------------------------
// Make generators, but only once
//-------------------------------------------------------------------------------------------------------------------
static void init_gens()
{
    std::call_once(init_gens_once_flag,
        [&](){

        // sanity check the generators
        static_assert(static_cast<unsigned char>(G.data[0]) == 0x58, "compile-time constant sanity check");
        static_assert(static_cast<unsigned char>(H.data[0]) == 0x8b, "compile-time constant sanity check");
        static_assert(static_cast<unsigned char>(T.data[0]) == 0x61, "compile-time constant sanity check");
        static_assert(static_cast<unsigned char>(U.data[0]) == 0x50, "compile-time constant sanity check");
        static_assert(static_cast<unsigned char>(V.data[0]) == 0x69, "compile-time constant sanity check");

        // build ge_p3 representations of generators
        const int G_deserialize = ge_frombytes_vartime(&G_p3, to_bytes(G));
        const int H_deserialize = ge_frombytes_vartime(&H_p3, to_bytes(H));
        const int T_deserialize = ge_frombytes_vartime(&T_p3, to_bytes(T));
        const int U_deserialize = ge_frombytes_vartime(&U_p3, to_bytes(U));
        const int V_deserialize = ge_frombytes_vartime(&V_p3, to_bytes(V));

        (void)G_deserialize; assert(G_deserialize == 0);
        (void)H_deserialize; assert(H_deserialize == 0);
        (void)T_deserialize; assert(T_deserialize == 0);
        (void)U_deserialize; assert(U_deserialize == 0);
        (void)V_deserialize; assert(V_deserialize == 0);

        // get cached versions
        ge_p3_to_cached(&G_cached, &G_p3);
        ge_p3_to_cached(&H_cached, &H_p3);
        ge_p3_to_cached(&T_cached, &T_p3);
        ge_p3_to_cached(&U_cached, &U_p3);
        ge_p3_to_cached(&V_cached, &V_p3);

        // in debug mode, check that generators are reproducible
        (void)reproduce_generator_G; assert(reproduce_generator_G() == G);
        (void)reproduce_generator_H; assert(reproduce_generator_H() == H);
        (void)reproduce_generator_T; assert(reproduce_generator_T() == T);
        (void)reproduce_generator_U; assert(reproduce_generator_U() == U);
        (void)reproduce_generator_V; assert(reproduce_generator_V() == V);

    });
}
//-------------------------------------------------------------------------------------------------------------------
public_key get_G()
{
    return G;
}
//-------------------------------------------------------------------------------------------------------------------
public_key get_H()
{
    return H;
}
//-------------------------------------------------------------------------------------------------------------------
public_key get_T()
{
    return T;
}
//-------------------------------------------------------------------------------------------------------------------
public_key get_U()
{
    return U;
}
//-------------------------------------------------------------------------------------------------------------------
public_key get_V()
{
    return V;
}
//-------------------------------------------------------------------------------------------------------------------
ge_p3 get_G_p3()
{
    init_gens();
    return G_p3;
}
//-------------------------------------------------------------------------------------------------------------------
ge_p3 get_H_p3()
{
    init_gens();
    return H_p3;
}
//-------------------------------------------------------------------------------------------------------------------
ge_p3 get_T_p3()
{
    init_gens();
    return T_p3;
}
//-------------------------------------------------------------------------------------------------------------------
ge_p3 get_U_p3()
{
    init_gens();
    return U_p3;
}
//-------------------------------------------------------------------------------------------------------------------
ge_p3 get_V_p3()
{
    init_gens();
    return V_p3;
}
//-------------------------------------------------------------------------------------------------------------------
ge_cached get_G_cached()
{
    init_gens();
    return G_cached;
}
//-------------------------------------------------------------------------------------------------------------------
ge_cached get_H_cached()
{
    init_gens();
    return H_cached;
}
//-------------------------------------------------------------------------------------------------------------------
ge_cached get_T_cached()
{
    init_gens();
    return T_cached;
}
//-------------------------------------------------------------------------------------------------------------------
ge_cached get_U_cached()
{
    init_gens();
    return U_cached;
}
//-------------------------------------------------------------------------------------------------------------------
ge_cached get_V_cached()
{
    init_gens();
    return V_cached;
}
//-------------------------------------------------------------------------------------------------------------------
} //namespace crypto