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// Copyright (c) 2019, Google Inc.
// Portions Copyright 2020 Brian Smith.
//
// Permission to use, copy, modify, and/or distribute this software for any
// purpose with or without fee is hereby granted, provided that the above
// copyright notice and this permission notice appear in all copies.
//
// THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
// WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
// SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
// WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
// OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
// CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
// This file is based on BoringSSL's gcm_nohw.c.
// This file contains a constant-time implementation of GHASH based on the notes
// in https://bearssl.org/constanttime.html#ghash-for-gcm and the reduction
// algorithm described in
// https://crypto.stanford.edu/RealWorldCrypto/slides/gueron.pdf.
//
// Unlike the BearSSL notes, we use u128 in the 64-bit implementation.
use super::{super::Block, Xi};
use crate::endian::BigEndian;
use core::convert::TryInto;
#[cfg(target_pointer_width = "64")]
fn gcm_mul64_nohw(a: u64, b: u64) -> (u64, u64) {
#[inline(always)]
fn lo(a: u128) -> u64 {
a as u64
}
#[inline(always)]
fn hi(a: u128) -> u64 {
lo(a >> 64)
}
#[inline(always)]
fn mul(a: u64, b: u64) -> u128 {
u128::from(a) * u128::from(b)
}
// One term every four bits means the largest term is 64/4 = 16, which barely
// overflows into the next term. Using one term every five bits would cost 25
// multiplications instead of 16. It is faster to mask off the bottom four
// bits of |a|, giving a largest term of 60/4 = 15, and apply the bottom bits
// separately.
let a0 = a & 0x1111111111111110;
let a1 = a & 0x2222222222222220;
let a2 = a & 0x4444444444444440;
let a3 = a & 0x8888888888888880;
let b0 = b & 0x1111111111111111;
let b1 = b & 0x2222222222222222;
let b2 = b & 0x4444444444444444;
let b3 = b & 0x8888888888888888;
let c0 = mul(a0, b0) ^ mul(a1, b3) ^ mul(a2, b2) ^ mul(a3, b1);
let c1 = mul(a0, b1) ^ mul(a1, b0) ^ mul(a2, b3) ^ mul(a3, b2);
let c2 = mul(a0, b2) ^ mul(a1, b1) ^ mul(a2, b0) ^ mul(a3, b3);
let c3 = mul(a0, b3) ^ mul(a1, b2) ^ mul(a2, b1) ^ mul(a3, b0);
// Multiply the bottom four bits of |a| with |b|.
let a0_mask = 0u64.wrapping_sub(a & 1);
let a1_mask = 0u64.wrapping_sub((a >> 1) & 1);
let a2_mask = 0u64.wrapping_sub((a >> 2) & 1);
let a3_mask = 0u64.wrapping_sub((a >> 3) & 1);
let extra = u128::from(a0_mask & b)
^ (u128::from(a1_mask & b) << 1)
^ (u128::from(a2_mask & b) << 2)
^ (u128::from(a3_mask & b) << 3);
let lo = (lo(c0) & 0x1111111111111111)
^ (lo(c1) & 0x2222222222222222)
^ (lo(c2) & 0x4444444444444444)
^ (lo(c3) & 0x8888888888888888)
^ lo(extra);
let hi = (hi(c0) & 0x1111111111111111)
^ (hi(c1) & 0x2222222222222222)
^ (hi(c2) & 0x4444444444444444)
^ (hi(c3) & 0x8888888888888888)
^ hi(extra);
(lo, hi)
}
#[cfg(not(target_pointer_width = "64"))]
fn gcm_mul32_nohw(a: u32, b: u32) -> u64 {
#[inline(always)]
fn mul(a: u32, b: u32) -> u64 {
u64::from(a) * u64::from(b)
}
// One term every four bits means the largest term is 32/4 = 8, which does not
// overflow into the next term.
let a0 = a & 0x11111111;
let a1 = a & 0x22222222;
let a2 = a & 0x44444444;
let a3 = a & 0x88888888;
let b0 = b & 0x11111111;
let b1 = b & 0x22222222;
let b2 = b & 0x44444444;
let b3 = b & 0x88888888;
let c0 = mul(a0, b0) ^ mul(a1, b3) ^ mul(a2, b2) ^ mul(a3, b1);
let c1 = mul(a0, b1) ^ mul(a1, b0) ^ mul(a2, b3) ^ mul(a3, b2);
let c2 = mul(a0, b2) ^ mul(a1, b1) ^ mul(a2, b0) ^ mul(a3, b3);
let c3 = mul(a0, b3) ^ mul(a1, b2) ^ mul(a2, b1) ^ mul(a3, b0);
(c0 & 0x1111111111111111)
| (c1 & 0x2222222222222222)
| (c2 & 0x4444444444444444)
| (c3 & 0x8888888888888888)
}
#[cfg(not(target_pointer_width = "64"))]
fn gcm_mul64_nohw(a: u64, b: u64) -> (u64, u64) {
#[inline(always)]
fn lo(a: u64) -> u32 {
a as u32
}
#[inline(always)]
fn hi(a: u64) -> u32 {
lo(a >> 32)
}
let a0 = lo(a);
let a1 = hi(a);
let b0 = lo(b);
let b1 = hi(b);
// Karatsuba multiplication.
let lo = gcm_mul32_nohw(a0, b0);
let hi = gcm_mul32_nohw(a1, b1);
let mid = gcm_mul32_nohw(a0 ^ a1, b0 ^ b1) ^ lo ^ hi;
(lo ^ (mid << 32), hi ^ (mid >> 32))
}
pub(super) fn init(xi: [u64; 2]) -> super::u128 {
// We implement GHASH in terms of POLYVAL, as described in RFC8452. This
// avoids a shift by 1 in the multiplication, needed to account for bit
// reversal losing a bit after multiplication, that is,
// rev128(X) * rev128(Y) = rev255(X*Y).
//
// Per Appendix A, we run mulX_POLYVAL. Note this is the same transformation
// applied by |gcm_init_clmul|, etc. Note |Xi| has already been byteswapped.
//
// See also slide 16 of
// https://crypto.stanford.edu/RealWorldCrypto/slides/gueron.pdf
let mut lo = xi[1];
let mut hi = xi[0];
let mut carry = hi >> 63;
carry = 0u64.wrapping_sub(carry);
hi <<= 1;
hi |= lo >> 63;
lo <<= 1;
// The irreducible polynomial is 1 + x^121 + x^126 + x^127 + x^128, so we
// conditionally add 0xc200...0001.
lo ^= carry & 1;
hi ^= carry & 0xc200000000000000;
// This implementation does not use the rest of |Htable|.
super::u128 { lo, hi }
}
fn gcm_polyval_nohw(xi: &mut [u64; 2], h: super::u128) {
// Karatsuba multiplication. The product of |Xi| and |H| is stored in |r0|
// through |r3|. Note there is no byte or bit reversal because we are
// evaluating POLYVAL.
let (r0, mut r1) = gcm_mul64_nohw(xi[0], h.lo);
let (mut r2, mut r3) = gcm_mul64_nohw(xi[1], h.hi);
let (mut mid0, mut mid1) = gcm_mul64_nohw(xi[0] ^ xi[1], h.hi ^ h.lo);
mid0 ^= r0 ^ r2;
mid1 ^= r1 ^ r3;
r2 ^= mid1;
r1 ^= mid0;
// Now we multiply our 256-bit result by x^-128 and reduce. |r2| and
// |r3| shifts into position and we must multiply |r0| and |r1| by x^-128. We
// have:
//
// 1 = x^121 + x^126 + x^127 + x^128
// x^-128 = x^-7 + x^-2 + x^-1 + 1
//
// This is the GHASH reduction step, but with bits flowing in reverse.
// The x^-7, x^-2, and x^-1 terms shift bits past x^0, which would require
// another reduction steps. Instead, we gather the excess bits, incorporate
// them into |r0| and |r1| and reduce once. See slides 17-19
// of https://crypto.stanford.edu/RealWorldCrypto/slides/gueron.pdf.
r1 ^= (r0 << 63) ^ (r0 << 62) ^ (r0 << 57);
// 1
r2 ^= r0;
r3 ^= r1;
// x^-1
r2 ^= r0 >> 1;
r2 ^= r1 << 63;
r3 ^= r1 >> 1;
// x^-2
r2 ^= r0 >> 2;
r2 ^= r1 << 62;
r3 ^= r1 >> 2;
// x^-7
r2 ^= r0 >> 7;
r2 ^= r1 << 57;
r3 ^= r1 >> 7;
*xi = [r2, r3];
}
pub(super) fn gmult(xi: &mut Xi, h: super::u128) {
with_swapped_xi(xi, |swapped| {
gcm_polyval_nohw(swapped, h);
})
}
pub(super) fn ghash(xi: &mut Xi, h: super::u128, input: &[u8]) {
with_swapped_xi(xi, |swapped| {
input.chunks_exact(16).for_each(|inp| {
swapped[0] ^= u64::from_be_bytes(inp[8..].try_into().unwrap());
swapped[1] ^= u64::from_be_bytes(inp[..8].try_into().unwrap());
gcm_polyval_nohw(swapped, h);
});
});
}
#[inline]
fn with_swapped_xi(Xi(xi): &mut Xi, f: impl FnOnce(&mut [u64; 2])) {
let unswapped = xi.u64s_be_to_native();
let mut swapped: [u64; 2] = [unswapped[1], unswapped[0]];
f(&mut swapped);
*xi = Block::from_u64_be(BigEndian::from(swapped[1]), BigEndian::from(swapped[0]))
}