polyval/backend/intrinsics/

x86.rs

//! VPCLMULQDQ optimized POLYVAL implementation using R/F Algorithm
//! Adapted from the implementation in the Apache 2.0 + MIT-licensed HPCrypt library
//! Copyright (c) 2024 HPCrypt Contributors
//!
//! Uses the R/F algorithm from "Efficient GHASH Implementation Using CLMUL":
//! - 4 CLMULs per block for multiplication (R and F terms)
//! - 1 CLMUL for reduction (Lemma 3)
//! - 4-block aggregated processing with single reduction
//!
//! Key equations:
//! - D = swap(H) ⊕ (H0 × P1)
//! - R = M0×D1 ⊕ M1×H1
//! - F = M0×D0 ⊕ M1×H0
//! - Result = R ⊕ F1 ⊕ (x^64×F0) ⊕ (P1×F0)
//!
//! POLYVAL operates in GF(2^128) with polynomial x^128 + x^127 + x^126 + x^121 + 1
//! Unlike GHASH, POLYVAL uses little-endian byte ordering (no byte swap needed).
//!
//! <https://eprint.iacr.org/2025/2171.pdf>

#![allow(unsafe_op_in_unsafe_fn)]

use super::ExpandedKey;
use crate::{Block, ParBlocks, field_element::FieldElement};

#[cfg(target_arch = "x86")]
use core::arch::x86::*;
#[cfg(target_arch = "x86_64")]
use core::arch::x86_64::*;

/// P1 polynomial: x^63 + x^62 + x^57 = 0xC200000000000000
const P1: u64 = 0xC200000000000000;

cpufeatures::new!(clmul, "avx", "pclmulqdq");
pub(crate) use clmul::InitToken;

/// Byte array which is the inner type of `FieldElement`
type ByteArray = [u8; 16];

impl FieldElement {
    #[target_feature(enable = "sse2")]
    #[inline]
    unsafe fn from_m128i(reg: __m128i) -> Self {
        let mut out = ByteArray::default();
        _mm_storeu_si128(out.as_mut_ptr().cast(), reg);
        out.into()
    }

    #[target_feature(enable = "sse2")]
    #[inline]
    unsafe fn to_m128i(self) -> __m128i {
        load_bytes(&self.into())
    }
}

/// Convert 16 bytes into `__m128i`.
///
/// # Safety
/// Requires SSE2 support
#[target_feature(enable = "sse2")]
#[inline]
unsafe fn load_bytes(bytes: &ByteArray) -> __m128i {
    _mm_loadu_si128(bytes.as_ptr().cast())
}

/// Update with a single block (5 CLMULs)
///
/// # Safety
/// Requires PCLMULQDQ support with VEX operands.
#[target_feature(enable = "avx", enable = "pclmulqdq")]
#[inline]
pub(super) unsafe fn proc_block(
    key: &ExpandedKey,
    acc: FieldElement,
    block: &Block,
) -> FieldElement {
    let data = load_bytes(&block.0);

    // XOR with accumulator
    let y = _mm_xor_si128(acc.to_m128i(), data);

    // Multiply by H using R/F algorithm
    FieldElement::from_m128i(gf128_mul_rf(y, key.h1.to_m128i(), key.d1.to_m128i()))
}

/// Process 4 blocks with R/F algorithm and aggregated reduction
///
/// Uses 16 CLMULs for multiplication (4 per block) + 1 CLMUL for reduction = 17 CLMULs total
#[target_feature(enable = "avx", enable = "pclmulqdq")]
#[inline]
pub(super) unsafe fn proc_par_blocks(
    key: &ExpandedKey,
    acc: FieldElement,
    par_blocks: &ParBlocks,
) -> FieldElement {
    // Load all 4 blocks (no byte swap for POLYVAL)
    let m0 = load_bytes(&par_blocks[0].0);
    let m1 = load_bytes(&par_blocks[1].0);
    let m2 = load_bytes(&par_blocks[2].0);
    let m3 = load_bytes(&par_blocks[3].0);

    // XOR first block with accumulator
    let y0 = _mm_xor_si128(acc.to_m128i(), m0);

    // R/F multiply all 4 blocks (16 CLMULs)
    let (r0, f0) = rf_mul_unreduced(y0, key.h4.to_m128i(), key.d4.to_m128i());
    let (r1, f1) = rf_mul_unreduced(m1, key.h3.to_m128i(), key.d3.to_m128i());
    let (r2, f2) = rf_mul_unreduced(m2, key.h2.to_m128i(), key.d2.to_m128i());
    let (r3, f3) = rf_mul_unreduced(m3, key.h1.to_m128i(), key.d1.to_m128i());

    // Aggregate R and F values
    let r = _mm_xor_si128(_mm_xor_si128(r0, r1), _mm_xor_si128(r2, r3));
    let f = _mm_xor_si128(_mm_xor_si128(f0, f1), _mm_xor_si128(f2, f3));

    // Single reduction (1 CLMUL)
    FieldElement::from_m128i(reduce_rf(r, f))
}

/// Create a new POLYVAL key with R/F algorithm
///
/// # Safety
/// Requires PCLMULQDQ support with VEX operands.
#[target_feature(enable = "avx", enable = "pclmulqdq")]
pub(super) unsafe fn expand_key(h: &[u8; 16]) -> ExpandedKey {
    let h1 = load_bytes(h);
    let d1 = compute_d(h1);

    // Compute powers using R/F multiplication
    let h2 = gf128_mul_rf(h1, h1, d1);
    let d2 = compute_d(h2);

    let h3 = gf128_mul_rf(h2, h1, d1);
    let d3 = compute_d(h3);

    let h4 = gf128_mul_rf(h2, h2, d2);
    let d4 = compute_d(h4);

    ExpandedKey {
        h1: FieldElement::from_m128i(h1),
        d1: FieldElement::from_m128i(d1),
        h2: FieldElement::from_m128i(h2),
        d2: FieldElement::from_m128i(d2),
        h3: FieldElement::from_m128i(h3),
        d3: FieldElement::from_m128i(d3),
        h4: FieldElement::from_m128i(h4),
        d4: FieldElement::from_m128i(d4),
    }
}

/// Compute D from H using the R/F algorithm
///
/// D = swap(H) ⊕ (H0 × P1)
#[target_feature(enable = "avx", enable = "pclmulqdq")]
#[inline]
unsafe fn compute_d(h: __m128i) -> __m128i {
    // TODO(tarcieri): P1.cast_signed() when MSRV 1.87+
    #[allow(clippy::cast_possible_wrap)]
    let p = _mm_set_epi64x(P1 as i64, 0);

    // Swap halves: [H1 : H0] -> [H0 : H1]
    let h_swap = _mm_shuffle_epi32(h, 0x4e);

    // T = H0 × P1
    let t = _mm_clmulepi64_si128(h, p, 0x10);

    // D = swap(H) ⊕ T
    _mm_xor_si128(h_swap, t)
}

/// R/F multiplication using 4 CLMULs per block
///
/// Given M = [M1 : M0] and precomputed H = [H1 : H0], D = [D1 : D0]:
/// - R = M0×D1 ⊕ M1×H1 (2 CLMULs)
/// - F = M0×D0 ⊕ M1×H0 (2 CLMULs)
///
/// Returns (R, F) for later reduction
#[target_feature(enable = "avx", enable = "pclmulqdq")]
#[inline]
unsafe fn rf_mul_unreduced(m: __m128i, h: __m128i, d: __m128i) -> (__m128i, __m128i) {
    // R = M0×D1 ⊕ M1×H1
    let r0 = _mm_clmulepi64_si128(m, d, 0x10); // M0 × D1
    let r1 = _mm_clmulepi64_si128(m, h, 0x11); // M1 × H1
    let r = _mm_xor_si128(r0, r1);

    // F = M0×D0 ⊕ M1×H0
    let f0 = _mm_clmulepi64_si128(m, d, 0x00); // M0 × D0
    let f1 = _mm_clmulepi64_si128(m, h, 0x01); // M1 × H0
    let f = _mm_xor_si128(f0, f1);

    (r, f)
}

/// Reduction using Lemma 3: Result = R ⊕ F1 ⊕ (x^64×F0) ⊕ (P1×F0)
///
/// Uses 1 CLMUL for reduction
#[target_feature(enable = "avx", enable = "pclmulqdq")]
#[inline]
unsafe fn reduce_rf(r: __m128i, f: __m128i) -> __m128i {
    // TODO(tarcieri): P1.cast_signed() when MSRV 1.87+
    #[allow(clippy::cast_possible_wrap)]
    let p1 = _mm_set_epi64x(0, P1 as i64);

    // F1 in low position
    let f1 = _mm_srli_si128(f, 8);

    // x^64×F0 (shift F0 to high position)
    let f0_shifted = _mm_slli_si128(f, 8);

    // P1×F0
    let p1_f0 = _mm_clmulepi64_si128(f, p1, 0x00);

    // Result = R ⊕ F1 ⊕ (x^64×F0) ⊕ (P1×F0)
    let result = _mm_xor_si128(r, f1);
    let result = _mm_xor_si128(result, f0_shifted);
    _mm_xor_si128(result, p1_f0)
}

/// Complete R/F multiplication with reduction (5 CLMULs total)
#[target_feature(enable = "avx", enable = "pclmulqdq")]
#[inline]
unsafe fn gf128_mul_rf(m: __m128i, h: __m128i, d: __m128i) -> __m128i {
    let (r, f) = rf_mul_unreduced(m, h, d);
    reduce_rf(r, f)
}