libdpf/examples/grotto/repr_and_twist.cpp

#include <cstdint>
#include <iostream>
#include <vector>

#include "grotto.hpp"

namespace
{

std::uint64_t pow_u64(std::uint64_t base, std::uint64_t exp)
{
    std::uint64_t acc = 1;
    while (exp != 0)
    {
        if (exp & 1u)
            acc *= base;
        base *= base;
        exp >>= 1;
    }
    return acc;
}

}  // namespace

/// Representation shift (Fibonacci / geometric / CRC) and twisted monomials.
int main()
{
    //! [repr-and-twist]
    // --- Representation shift: Fibonacci checkpoint ----------------------
    // Dealer keys S_c = (F_{c+1}, F_c). After eta opens, each party applies
    // the public companion-matrix power M^kappa to its share of S_c.
    const std::uint8_t center = 10;
    const std::uint8_t eta = 5;
    const std::uint8_t point = static_cast<std::uint8_t>(center + eta);  // 15
    const auto fib_state = grotto::offset_repr_fibonacci_state(center);
    const auto M = grotto::offset_repr_fibonacci_matrix();
    auto fib_keys = grotto::make_offset_repr_keys<std::uint8_t>(center, fib_state);
    const std::vector<std::uint8_t> knots{0};

    const auto f0 = grotto::offset_repr_eval<0>(fib_keys, M, knots, eta);
    const auto f1 = grotto::offset_repr_eval<1>(fib_keys, M, knots, eta);
    const std::vector<std::uint64_t> S{f0[0] + f1[0], f0[1] + f1[1]};

    // Geometric twin: 1x1 matrix [lambda] advances lambda^c by lambda^kappa.
    const std::uint64_t lambda_geo = 3;
    const auto G = grotto::offset_repr_geometric_matrix(lambda_geo);
    auto geo_keys = grotto::make_offset_repr_keys<std::uint8_t>(
        center, {pow_u64(lambda_geo, center)});
    const auto g0 = grotto::offset_repr_eval<0>(geo_keys, G, knots, eta);
    const auto g1 = grotto::offset_repr_eval<1>(geo_keys, G, knots, eta);
    const std::uint64_t geo = g0[0] + g1[0];

    // Clear CRC-32 jump documents the GF(2) twin (XOR shares, not additive).
    const std::uint32_t crc_seed = 0x12345678u;
    const std::uint32_t crc_jumped = grotto::offset_repr_crc32_jump(crc_seed, 64);

    // --- Twisted monomials: (a0 + a1 x + a2 x^2) * lambda^x -------------
    const std::uint64_t lambda = 3;
    const std::size_t degree = 2;
    auto twist_keys = grotto::make_offset_twist_keys<std::uint8_t>(
        center, degree, lambda);
    // h(x) = (2 + 5x + x^2) * 3^x
    const std::vector<std::uint64_t> coeff{2, 5, 1};
    const std::uint64_t twisted =
        grotto::offset_twist_eval<0>(twist_keys, knots, coeff, eta)
        + grotto::offset_twist_eval<1>(twist_keys, knots, coeff, eta);

    // Dyadic decay: masked carry shift. The sum of the shares is the shifted value.
    auto half_keys = grotto::make_offset_twist_keys<std::uint8_t>(
        center, degree, grotto::twist_half);
    const std::uint64_t half =
        grotto::offset_twist_eval<0>(half_keys, knots, coeff, eta)
        + grotto::offset_twist_eval<1>(half_keys, knots, coeff, eta);

    // Closed form sum_{k=1}^n k * lambda^k from the same twisted table.
    const std::uint64_t ag = grotto::offset_twist_arithmetico_geometric(point, lambda);
    //! [repr-and-twist]

    const auto expect_S = grotto::offset_repr_fibonacci_state(point);
    if (S != expect_S)
    {
        std::cerr << "fibonacci state\n";
        return 1;
    }
    if (geo != pow_u64(lambda_geo, point))
    {
        std::cerr << "geometric\n";
        return 1;
    }
    std::uint64_t expect_t = 0;
    std::uint64_t xp = 1;
    for (std::uint64_t c : coeff)
    {
        expect_t += c * xp;
        xp *= point;
    }
    expect_t *= pow_u64(lambda, point);
    if (twisted != expect_t)
    {
        std::cerr << "twisted poly\n";
        return 1;
    }
    std::uint64_t expect_h = 0;
    xp = 1;
    for (std::uint64_t c : coeff)
    {
        expect_h += c * xp;
        xp *= point;
    }
    expect_h >>= point;
    if (half != expect_h)
    {
        std::cerr << "twist half\n";
        return 1;
    }
    std::uint64_t expect_ag = 0;
    for (std::uint64_t k = 1; k <= point; ++k)
        expect_ag += k * pow_u64(lambda, k);
    if (ag != expect_ag)
    {
        std::cerr << "arithmetico-geometric\n";
        return 1;
    }
    if (crc_jumped == 0 && crc_seed != 0)
    {
        // Jump can legally land on zero; only used as a smoke output.
    }

    std::cout << S[1] << " " << geo << " " << twisted << " " << half << " "
              << ag << " " << crc_jumped << "\n";
    return 0;
}