keccak.cpp

Go to the documentation of this file.

// === AUDIT STATUS ===
// internal:    { status: Complete, auditors: [Nishat], commit: }
// external_1:  { status: not started, auditors: [], commit: }
// external_2:  { status: not started, auditors: [], commit: }
// =====================
 
#include "keccak.hpp"
#include "barretenberg/common/assert.hpp"
#include "barretenberg/common/constexpr_utils.hpp"
#include "barretenberg/numeric/bitop/sparse_form.hpp"
#include "barretenberg/stdlib/primitives/logic/logic.hpp"
#include "barretenberg/stdlib/primitives/plookup/plookup.hpp"
#include "barretenberg/stdlib_circuit_builders/plookup_tables/keccak/keccak_rho.hpp"
#include "barretenberg/stdlib_circuit_builders/plookup_tables/keccak/keccak_theta.hpp"
namespace bb::stdlib {
 
using namespace bb::plookup;
 
template <typename Builder>
template <size_t lane_index>
field_t<Builder> keccak<Builder>::normalize_and_rotate(const field_ct& limb, field_ct& msb)
{
    // left_bits = the number of bits that wrap around 11^{KECCAK_LANE_SIZE} (left_bits)
    constexpr size_t left_bits = ROTATIONS[lane_index];
 
    // right_bits = the number of bits that don't wrap
    constexpr size_t right_bits = KECCAK_LANE_SIZE - ROTATIONS[lane_index];
 
    // Matches the maximum bits per slice (Rho<>::MAXIMUM_MULTITABLE_BITS) used by KECCAK_RHO multitables
    constexpr size_t max_bits_per_table = plookup::keccak_tables::Rho<>::MAXIMUM_MULTITABLE_BITS;
 
    // compute the number of lookups required for our left and right bit slices
    constexpr size_t num_left_tables = left_bits / max_bits_per_table + (left_bits % max_bits_per_table > 0 ? 1 : 0);
    constexpr size_t num_right_tables = right_bits / max_bits_per_table + (right_bits % max_bits_per_table > 0 ? 1 : 0);
 
    // get the numerical value of the left and right bit slices
    // (lookup table input values derived from left / right)
    uint256_t input = limb.get_value();
    constexpr uint256_t slice_divisor = BASE.pow(right_bits);
    const auto [left, right] = input.divmod(slice_divisor);
 
    // compute the normalized values for the left and right bit slices
    // (lookup table output values derived from left_normalised / right_normalized)
    uint256_t left_normalized = normalize_sparse(left);
    uint256_t right_normalized = normalize_sparse(right);
 
    plookup::ReadData<bb::fr> lookup;
 
    // compute plookup witness values for a given slice
    // (same lambda can be used to compute witnesses for left and right slices)
    auto compute_lookup_witnesses_for_limb = [&]<size_t limb_bits, size_t num_lookups>(uint256_t& normalized) {
        // (use a constexpr loop to make some pow and div operations compile-time)
        bb::constexpr_for<0, num_lookups, 1>([&]<size_t i> {
            constexpr size_t num_bits_processed = i * max_bits_per_table;
 
            // How many bits can this slice contain?
            // We want to implicitly range-constrain `normalized < 11^{limb_bits}`,
            // which means potentially using a lookup table that is not of size 11^{max_bits_per_table}
            // for the most-significant slice
            constexpr size_t bit_slice = (num_bits_processed + max_bits_per_table > limb_bits)
                                             ? limb_bits % max_bits_per_table
                                             : max_bits_per_table;
 
            // current column values are tracked via 'input' and 'normalized'
            lookup[ColumnIdx::C1].push_back(input);
            lookup[ColumnIdx::C2].push_back(normalized);
 
            constexpr uint64_t divisor = numeric::pow64(static_cast<uint64_t>(BASE), bit_slice);
            constexpr uint64_t msb_divisor = divisor / static_cast<uint64_t>(BASE);
 
            // compute the value of the most significant bit of this slice and store in C3
            const auto [normalized_quotient, normalized_slice] = normalized.divmod(divisor);
 
            // 256-bit divisions are expensive! cast to u64s when we don't need the extra bits
            const uint64_t normalized_msb = (static_cast<uint64_t>(normalized_slice) / msb_divisor);
            lookup[ColumnIdx::C3].push_back(normalized_msb);
 
            // We need to provide a key/value object for this lookup in order for the Builder
            // to compute the plookup sorted list commitment
            const auto [input_quotient, input_slice] = input.divmod(divisor);
            lookup.lookup_entries.push_back(
                { { static_cast<uint64_t>(input_slice), 0 }, { normalized_slice, normalized_msb } });
 
            // reduce the input and output by 11^{bit_slice}
            input = input_quotient;
            normalized = normalized_quotient;
        });
    };
 
    // template lambda syntax is a little funky.
    // Need to explicitly write `.template operator()` (instead of just `()`).
    // Otherwise compiler cannot distinguish between `>` symbol referring to closing the template parameter list,
    // OR `>` being a greater-than operator :/
    compute_lookup_witnesses_for_limb.template operator()<right_bits, num_right_tables>(right_normalized);
    compute_lookup_witnesses_for_limb.template operator()<left_bits, num_left_tables>(left_normalized);
 
    // Call builder method to create plookup constraints.
    // The MultiTable table index can be derived from `lane_idx`
    // Each lane_idx has a different rotation amount, which changes sizes of left/right slices
    // and therefore the selector constants required (i.e. the Q1, Q2, Q3 values in the earlier example)
    const auto accumulator_witnesses = limb.context->create_gates_from_plookup_accumulators(
        (plookup::MultiTableId)((size_t)KECCAK_NORMALIZE_AND_ROTATE + lane_index), lookup, limb.get_witness_index());
 
    // extract the most significant bit of the normalized output from the final lookup entry in column C3
    msb = field_ct::from_witness_index(limb.get_context(),
                                       accumulator_witnesses[ColumnIdx::C3][num_left_tables + num_right_tables - 1]);
 
    // Extract the witness that maps to the normalized right slice
    const field_t<Builder> right_output =
        field_t<Builder>::from_witness_index(limb.get_context(), accumulator_witnesses[ColumnIdx::C2][0]);
 
    if (num_left_tables == 0) {
        // if the left slice size is 0 bits (i.e. no rotation), return `right_output`
        return right_output;
    } else {
        // Extract the normalized left slice
        const field_t<Builder> left_output = field_t<Builder>::from_witness_index(
            limb.get_context(), accumulator_witnesses[ColumnIdx::C2][num_right_tables]);
 
        // Stitch the right/left slices together to create our rotated output
        constexpr uint256_t shift = BASE.pow(ROTATIONS[lane_index]);
        return (left_output + right_output * shift);
    }
}
 
template <typename Builder> void keccak<Builder>::compute_twisted_state(keccak_state& internal)
{
    for (size_t i = 0; i < NUM_KECCAK_LANES; ++i) {
        internal.twisted_state[i] = ((internal.state[i] * 11) + internal.state_msb[i]).normalize();
    }
}
 
template <typename Builder> void keccak<Builder>::theta(keccak_state& internal)
{
    std::array<field_ct, 5> C;
    std::array<field_ct, 5> D;
 
    auto& state = internal.state;
    const auto& twisted_state = internal.twisted_state;
    for (size_t i = 0; i < 5; ++i) {
 
        C[i] = field_ct::accumulate({ twisted_state[i],
                                      twisted_state[5 + i],
                                      twisted_state[10 + i],
                                      twisted_state[15 + i],
                                      twisted_state[20 + i] });
    }
 
    for (size_t i = 0; i < 5; ++i) {
        const auto non_shifted_equivalent = (C[(i + 4) % 5]);
        const auto shifted_equivalent = C[(i + 1) % 5] * BASE;
        D[i] = (non_shifted_equivalent + shifted_equivalent);
    }
 
    static constexpr uint256_t divisor = BASE.pow(KECCAK_LANE_SIZE);
    static constexpr uint256_t multiplicand = BASE.pow(KECCAK_LANE_SIZE + 1);
    for (size_t i = 0; i < 5; ++i) {
        uint256_t D_native = D[i].get_value();
        const auto [D_quotient, lo_native] = D_native.divmod(BASE);
        const uint256_t hi_native = D_quotient / divisor;
        const uint256_t mid_native = D_quotient - hi_native * divisor;
 
        field_ct hi(witness_ct(internal.context, hi_native));
        field_ct mid(witness_ct(internal.context, mid_native));
        field_ct lo(witness_ct(internal.context, lo_native));
 
        // assert equal should cost 1 gate (multipliers are all constants)
        D[i].assert_equal((hi * multiplicand).add_two(mid * 11, lo));
        internal.context->create_small_range_constraint(hi.get_witness_index(), static_cast<uint64_t>(BASE));
        internal.context->create_small_range_constraint(lo.get_witness_index(), static_cast<uint64_t>(BASE));
 
        // If number of bits in KECCAK_THETA_OUTPUT table does NOT cleanly divide KECCAK_LANE_SIZE=64,
        // we need an additional range constraint to ensure that mid < 11^64
        static_assert(KECCAK_LANE_SIZE % plookup::keccak_tables::Theta::TABLE_BITS == 0,
                      "KECCAK_THETA_OUTPUT TABLE_BITS must divide KECCAK_LANE_SIZE.");
        D[i] = plookup_read<Builder>::read_from_1_to_2_table(KECCAK_THETA_OUTPUT, mid);
    }
 
    // compute state[j * 5 + i] XOR D[i] in base-11 representation
    for (size_t i = 0; i < 5; ++i) {
        for (size_t j = 0; j < 5; ++j) {
            state[j * 5 + i] = state[j * 5 + i] + D[i];
        }
    }
}
 
template <typename Builder> void keccak<Builder>::rho(keccak_state& internal)
{
    constexpr_for<0, NUM_KECCAK_LANES, 1>(
        [&]<size_t i>() { internal.state[i] = normalize_and_rotate<i>(internal.state[i], internal.state_msb[i]); });
}
 
template <typename Builder> void keccak<Builder>::pi(keccak_state& internal)
{
    std::array<field_ct, NUM_KECCAK_LANES> B;
 
    for (size_t j = 0; j < 5; ++j) {
        for (size_t i = 0; i < 5; ++i) {
            B[j * 5 + i] = internal.state[j * 5 + i];
        }
    }
 
    for (size_t y = 0; y < 5; ++y) {
        for (size_t x = 0; x < 5; ++x) {
            size_t u = (0 * x + 1 * y) % 5;
            size_t v = (2 * x + 3 * y) % 5;
 
            internal.state[v * 5 + u] = B[5 * y + x];
        }
    }
}
 
template <typename Builder> void keccak<Builder>::chi(keccak_state& internal)
{
    // (cost = 12 * 25 = 300?)
    auto& state = internal.state;
 
    for (size_t y = 0; y < 5; ++y) {
        std::array<field_ct, 5> lane_outputs;
        for (size_t x = 0; x < 5; ++x) {
            const auto A = state[y * 5 + x];
            const auto B = state[y * 5 + ((x + 1) % 5)];
            const auto C = state[y * 5 + ((x + 2) % 5)];
 
            // vv should cost 1 gate
            lane_outputs[x] = (A + A + CHI_OFFSET).add_two(-B, C);
        }
        for (size_t x = 0; x < 5; ++x) {
            // Normalize lane outputs and assign to internal.state
            auto accumulators = plookup_read<Builder>::get_lookup_accumulators(KECCAK_CHI_OUTPUT, lane_outputs[x]);
            internal.state[y * 5 + x] = accumulators[ColumnIdx::C2][0];
            internal.state_msb[y * 5 + x] = accumulators[ColumnIdx::C3][accumulators[ColumnIdx::C3].size() - 1];
        }
    }
}
 
template <typename Builder> void keccak<Builder>::iota(keccak_state& internal, size_t round)
{
    const field_ct xor_result = internal.state[0] + SPARSE_RC[round];
 
    // normalize lane value so that we don't overflow our base11 modulus boundary in the next round
    internal.state[0] = normalize_and_rotate<0>(xor_result, internal.state_msb[0]);
 
    // No need to add constraints to compute twisted repr if this is the last round
    if (round != NUM_KECCAK_ROUNDS - 1) {
        compute_twisted_state(internal);
    }
}
 
template <typename Builder> void keccak<Builder>::keccakf1600(keccak_state& internal)
{
    for (size_t i = 0; i < NUM_KECCAK_ROUNDS; ++i) {
        theta(internal);
        rho(internal);
        pi(internal);
        chi(internal);
        iota(internal, i);
    }
}
 
// Returns the keccak f1600 permutation of the input state
// We first convert the state into 'extended' representation, along with the 'twisted' state
// and then we call keccakf1600() with this keccak 'internal state'
// Finally, we convert back the state from the extented representation
template <typename Builder>
std::array<field_t<Builder>, keccak<Builder>::NUM_KECCAK_LANES> keccak<Builder>::permutation_opcode(
    std::array<field_t<Builder>, NUM_KECCAK_LANES> state, Builder* ctx)
{
    // populate keccak_state, convert our KECCAK_LANE_SIZE-bit lanes into an extended base-11 representation
    keccak_state internal;
    internal.context = ctx;
    for (size_t i = 0; i < state.size(); ++i) {
        const auto accumulators = plookup_read<Builder>::get_lookup_accumulators(KECCAK_FORMAT_INPUT, state[i]);
        internal.state[i] = accumulators[ColumnIdx::C2][0];
        internal.state_msb[i] = accumulators[ColumnIdx::C3][accumulators[ColumnIdx::C3].size() - 1];
    }
    compute_twisted_state(internal);
    keccakf1600(internal);
    // we convert back to the normal lanes
    return extended_2_normal(internal);
}
 
// Convert the 'extended' representation of the internal Keccak state into the usual array of KECCAK_LANE_SIZE bit lanes
template <typename Builder>
std::array<field_t<Builder>, keccak<Builder>::NUM_KECCAK_LANES> keccak<Builder>::extended_2_normal(
    keccak_state& internal)
{
    std::array<field_t<Builder>, NUM_KECCAK_LANES> conversion;
 
    // Each hash limb represents a little-endian integer.
    for (size_t i = 0; i < internal.state.size(); ++i) {
        field_ct output_limb = plookup_read<Builder>::read_from_1_to_2_table(KECCAK_FORMAT_OUTPUT, internal.state[i]);
        conversion[i] = output_limb;
    }
 
    return conversion;
}
 
template class keccak<bb::UltraCircuitBuilder>;
template class keccak<bb::MegaCircuitBuilder>;
 
} // namespace bb::stdlib