precomputed_tables_builder.hpp

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// === AUDIT STATUS ===
// internal:    { status: Complete, auditors: [Raju], commit: 2a49eb6 }
// external_1:  { status: not started, auditors: [], commit: }
// external_2:  { status: not started, auditors: [], commit: }
// =====================
 
#pragma once
 
#include "./eccvm_builder_types.hpp"
#include "barretenberg/common/assert.hpp"
 
namespace bb {
 
class ECCVMPointTablePrecomputationBuilder {
  public:
    using CycleGroup = bb::g1;
    using FF = grumpkin::fr;
    using Element = typename CycleGroup::element;
    using AffineElement = typename CycleGroup::affine_element;
 
    static constexpr size_t NUM_WNAF_DIGITS_PER_SCALAR = bb::eccvm::NUM_WNAF_DIGITS_PER_SCALAR;
    static constexpr size_t WNAF_DIGITS_PER_ROW = bb::eccvm::WNAF_DIGITS_PER_ROW;
    static constexpr size_t NUM_WNAF_DIGIT_BITS = bb::eccvm::NUM_WNAF_DIGIT_BITS;
    // Note that our implementation takes advantage of a numerical coincidence:
    // `NUM_WNAF_DIGITS_PER_SCALAR`/`WNAF_DIGITS_PER_ROW`, the number of rows per scalar multiplication, is the same as
    // |{P, 3P, ..., (2ʷ-1)P}| = 2ʷ⁻¹ == 8, which is basically the number of multiples of P we need to precompute. (To
    // be precise, we also compute 2P, but this occurs on every row.)
    struct PointTablePrecomputationRow {
        // s1, ..., s8 are each 2 bits, so they jointly encode 16 bits of information, which corresponds precisely to
        // the data of 4 wNAF digits. they are ordered from "highest order" to "lowest order". this means that s1s2
        // encodes the first (highest order) wNAF digit in consideration, and so on. the explicit encoding is: the
        // concatenation, s_{2i}s_{2i+1}, is naturally a number in {0, 1, ..., 15}; to obtain the corresponding wNAF
        // digit, multiply by 2 and subtract 15.
        int s1 = 0;
        int s2 = 0;
        int s3 = 0;
        int s4 = 0;
        int s5 = 0;
        int s6 = 0;
        int s7 = 0;
        int s8 = 0;
        bool skew = false;
        bool point_transition = false;
        uint32_t pc = 0;
        uint32_t round = 0;
        uint256_t scalar_sum = 0;
        AffineElement precompute_accumulator{
            0, 0
        }; // contains a precomputed element, i.e., something in {P, 3P, ..., 15P}.
        AffineElement precompute_double{ 0, 0 };
    };
 
    static std::vector<PointTablePrecomputationRow> compute_rows(
        const std::vector<bb::eccvm::ScalarMul<CycleGroup>>& ecc_muls)
    {
        static constexpr size_t num_rows_per_scalar = NUM_WNAF_DIGITS_PER_SCALAR / WNAF_DIGITS_PER_ROW;
        static_assert(num_rows_per_scalar == bb::eccvm::POINT_TABLE_SIZE / 2,
                      "precompute_accumulator fill loop assumes num_rows_per_scalar == POINT_TABLE_SIZE / 2");
        const size_t num_precompute_rows = num_rows_per_scalar * ecc_muls.size() + 1;
        std::vector<PointTablePrecomputationRow> precompute_state(num_precompute_rows);
 
        // start with empty row (shiftable polynomials must have 0 as first coefficient)
        precompute_state[0] = PointTablePrecomputationRow{};
 
        // current impl doesn't work if not 4
        static_assert(WNAF_DIGITS_PER_ROW == 4);
 
        parallel_for_range(ecc_muls.size(), [&](size_t start, size_t end) {
            for (size_t j = start; j < end; j++) {
                const auto& entry = ecc_muls[j];
                const auto& slices = entry.wnaf_digits;
                uint256_t scalar_sum = 0;
 
                for (size_t i = 0; i < num_rows_per_scalar; ++i) {
                    PointTablePrecomputationRow row;
                    const int slice0 = slices[i * WNAF_DIGITS_PER_ROW];
                    const int slice1 = slices[i * WNAF_DIGITS_PER_ROW + 1];
                    const int slice2 = slices[i * WNAF_DIGITS_PER_ROW + 2];
                    const int slice3 = slices[i * WNAF_DIGITS_PER_ROW + 3];
 
                    // {-15, -13. ..., 13, 15} --> {0, 1, ..., 15}
                    const int slice0base2 = (slice0 + 15) / 2;
                    const int slice1base2 = (slice1 + 15) / 2;
                    const int slice2base2 = (slice2 + 15) / 2;
                    const int slice3base2 = (slice3 + 15) / 2;
 
                    // convert into 2-bit chunks
                    row.s1 = slice0base2 >> 2;
                    row.s2 = slice0base2 & 3;
                    row.s3 = slice1base2 >> 2;
                    row.s4 = slice1base2 & 3;
                    row.s5 = slice2base2 >> 2;
                    row.s6 = slice2base2 & 3;
                    row.s7 = slice3base2 >> 2;
                    row.s8 = slice3base2 & 3;
                    bool last_row = (i == num_rows_per_scalar - 1);
 
                    row.skew = last_row ? entry.wnaf_skew : false;
 
                    row.scalar_sum = scalar_sum;
 
                    // N.B. we apply a constraint that requires slice1 to be positive for the 1st row of each scalar
                    // sum. This ensures we do not have WNAF representations of negative values
                    const int row_chunk = slice3 + slice2 * (1 << 4) + slice1 * (1 << 8) + slice0 * (1 << 12);
 
                    bool chunk_negative = row_chunk < 0;
 
                    scalar_sum = scalar_sum << (NUM_WNAF_DIGIT_BITS * WNAF_DIGITS_PER_ROW);
                    if (chunk_negative) {
                        scalar_sum -= static_cast<uint64_t>(-row_chunk);
                    } else {
                        scalar_sum += static_cast<uint64_t>(row_chunk);
                    }
                    row.round = static_cast<uint32_t>(i);
                    row.point_transition = last_row;
                    row.pc = entry.pc;
 
                    if (last_row) {
                        BB_ASSERT_EQ(scalar_sum - entry.wnaf_skew, entry.scalar);
                    }
                    // the last element of the `precomputed_table` field of a `ScalarMul` is the double of the point.
                    row.precompute_double = entry.precomputed_table[bb::eccvm::POINT_TABLE_SIZE];
                    // fill accumulator in reverse order i.e. first row = 15[P], then 13[P], ..., 1[P]
                    // note that this reflects a coincidence: the number of rows (per scalar multiplication) is
                    // the number of multiples that we need to precompute. Indeed, the latter is 2ʷ⁻¹, while the former
                    // depends both on w and on `NUM_SCALAR_BITS`.
                    row.precompute_accumulator = entry.precomputed_table[bb::eccvm::POINT_TABLE_SIZE - 1 - i];
                    precompute_state[j * num_rows_per_scalar + i + 1] = (row);
                }
            }
        });
        return precompute_state;
    }
};
} // namespace bb