ghash.h

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/*
 * Based on work by: Shay Gueron, Michael E. Kounavis, Erdinc Ozturk,
 *                   Vinodh Gopal, James Guilford, Tomasz Kantecki
 *
 * References:
 * [1] Vinodh Gopal et. al. Optimized Galois-Counter-Mode Implementation on
 *     Intel Architecture Processors. August, 2010
 * [2] Erdinc Ozturk et. al. Enabling High-Performance Galois-Counter-Mode on
 *     Intel Architecture Processors. October, 2012.
 * [3] intel-ipsec-mb library, https://github.com/01org/intel-ipsec-mb.git
 *
 * Definitions:
 *  GF    Galois Extension Field GF(2^128) - finite field where elements are
 *        represented as polynomials with coefficients in GF(2) with the
 *        highest degree of 127. Polynomials are represented as 128-bit binary
 *        numbers where each bit represents one coefficient.
 *        e.g. polynomial x^5 + x^3 + x + 1 is represented in binary 101011.
 *  H     hash key (128 bit)
 *  POLY  irreducible polynomial x^127 + x^7 + x^2 + x + 1
 *  RPOLY irreducible polynomial x^128 + x^127 + x^126 + x^121 + 1
 *  +     addition in GF, which equals to XOR operation
 *  *     multiplication in GF
 *
 * GF multiplication consists of 2 steps:
 *  - carry-less multiplication of two 128-bit operands into 256-bit result
 *  - reduction of 256-bit result into 128-bit with modulo POLY
 *
 * GHash is calculated on 128-bit blocks of data according to the following
 * formula:
 *    GH = (GH + data) * hash_key
 *
 * To avoid bit-reflection of data, this code uses GF multipication
 * with reversed polynomial:
 *   a * b * x^-127 mod RPOLY
 *
 * To improve computation speed table Hi is precomputed with powers of H',
 * where H' is calculated as H<<1 mod RPOLY.
 * This allows us to improve performance by deferring reduction. For example
 * to caclulate ghash of 4 128-bit blocks of data (b0, b1, b2, b3), we can do:
 *
 * __i128 Hi[4];
 * ghash_precompute (H, Hi, 4);
 *
 * ghash_data_t _gd, *gd = &_gd;
 * ghash_mul_first (gd, GH ^ b0, Hi[3]);
 * ghash_mul_next (gd, b1, Hi[2]);
 * ghash_mul_next (gd, b2, Hi[1]);
 * ghash_mul_next (gd, b3, Hi[0]);
 * ghash_reduce (gd);
 * ghash_reduce2 (gd);
 * GH = ghash_final (gd);
 *
 * Reduction step is split into 3 functions so it can be better interleaved
 * with other code, (i.e. with AES computation).
 */

#ifndef __ghash_h__
#define __ghash_h__

/* on AVX-512 systems we can save a clock cycle by using ternary logic
   instruction to calculate a XOR b XOR c */
static_always_inline __m128i
ghash_xor3 (__m128i a, __m128i b, __m128i c)
{
#if defined (__AVX512F__)
  return _mm_ternarylogic_epi32 (a, b, c, 0x96);
#endif
  return a ^ b ^ c;
}

typedef struct
{
  __m128i mid, hi, lo, tmp_lo, tmp_hi;
  int pending;
} ghash_data_t;

static const __m128i ghash_poly = { 1, 0xC200000000000000 };
static const __m128i ghash_poly2 = { 0x1C2000000, 0xC200000000000000 };

static_always_inline void
ghash_mul_first (ghash_data_t * gd, __m128i a, __m128i b)
{
  /* a1 * b1 */
  gd->hi = _mm_clmulepi64_si128 (a, b, 0x11);
  /* a0 * b0 */
  gd->lo = _mm_clmulepi64_si128 (a, b, 0x00);
  /* a0 * b1 ^ a1 * b0 */
  gd->mid = (_mm_clmulepi64_si128 (a, b, 0x01) ^
             _mm_clmulepi64_si128 (a, b, 0x10));

  /* set gd->pending to 0 so next invocation of ghash_mul_next(...) knows that
     there is no pending data in tmp_lo and tmp_hi */
  gd->pending = 0;
}

static_always_inline void
ghash_mul_next (ghash_data_t * gd, __m128i a, __m128i b)
{
  /* a1 * b1 */
  __m128i hi = _mm_clmulepi64_si128 (a, b, 0x11);
  /* a0 * b0 */
  __m128i lo = _mm_clmulepi64_si128 (a, b, 0x00);

  /* this branch will be optimized out by the compiler, and it allows us to
     reduce number of XOR operations by using ternary logic */
  if (gd->pending)
    {
      /* there is peding data from previous invocation so we can XOR */
      gd->hi = ghash_xor3 (gd->hi, gd->tmp_hi, hi);
      gd->lo = ghash_xor3 (gd->lo, gd->tmp_lo, lo);
      gd->pending = 0;
    }
  else
    {
      /* there is no peding data from previous invocation so we postpone XOR */
      gd->tmp_hi = hi;
      gd->tmp_lo = lo;
      gd->pending = 1;
    }

  /* gd->mid ^= a0 * b1 ^ a1 * b0  */
  gd->mid = ghash_xor3 (gd->mid,
                        _mm_clmulepi64_si128 (a, b, 0x01),
                        _mm_clmulepi64_si128 (a, b, 0x10));
}

static_always_inline void
ghash_reduce (ghash_data_t * gd)
{
  __m128i r;

  /* Final combination:
     gd->lo ^= gd->mid << 64
     gd->hi ^= gd->mid >> 64 */
  __m128i midl = _mm_slli_si128 (gd->mid, 8);
  __m128i midr = _mm_srli_si128 (gd->mid, 8);

  if (gd->pending)
    {
      gd->lo = ghash_xor3 (gd->lo, gd->tmp_lo, midl);
      gd->hi = ghash_xor3 (gd->hi, gd->tmp_hi, midr);
    }
  else
    {
      gd->lo ^= midl;
      gd->hi ^= midr;
    }

  r = _mm_clmulepi64_si128 (ghash_poly2, gd->lo, 0x01);
  gd->lo ^= _mm_slli_si128 (r, 8);
}

static_always_inline void
ghash_reduce2 (ghash_data_t * gd)
{
  gd->tmp_lo = _mm_clmulepi64_si128 (ghash_poly2, gd->lo, 0x00);
  gd->tmp_hi = _mm_clmulepi64_si128 (ghash_poly2, gd->lo, 0x10);
}

static_always_inline __m128i
ghash_final (ghash_data_t * gd)
{
  return ghash_xor3 (gd->hi, _mm_srli_si128 (gd->tmp_lo, 4),
                     _mm_slli_si128 (gd->tmp_hi, 4));
}

static_always_inline __m128i
ghash_mul (__m128i a, __m128i b)
{
  ghash_data_t _gd, *gd = &_gd;
  ghash_mul_first (gd, a, b);
  ghash_reduce (gd);
  ghash_reduce2 (gd);
  return ghash_final (gd);
}

static_always_inline void
ghash_precompute (__m128i H, __m128i * Hi, int count)
{
  __m128i r;
  /* calcullate H<<1 mod poly from the hash key */
  r = _mm_srli_epi64 (H, 63);
  H = _mm_slli_epi64 (H, 1);
  H |= _mm_slli_si128 (r, 8);
  r = _mm_srli_si128 (r, 8);
  r = _mm_shuffle_epi32 (r, 0x24);
  /* *INDENT-OFF* */
  r = _mm_cmpeq_epi32 (r, (__m128i) (u32x4) {1, 0, 0, 1});
  /* *INDENT-ON* */
  Hi[0] = H ^ (r & ghash_poly);

  /* calculate H^(i + 1) */
  for (int i = 1; i < count; i++)
    Hi[i] = ghash_mul (Hi[0], Hi[i - 1]);
}

#endif /* __ghash_h__ */

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