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50 * Based on work by: Shay Gueron, Michael E. Kounavis, Erdinc Ozturk,
51 * Vinodh Gopal, James Guilford, Tomasz Kantecki
54 * [1] Vinodh Gopal et. al. Optimized Galois-Counter-Mode Implementation on
55 * Intel Architecture Processors. August, 2010
56 * [2] Erdinc Ozturk et. al. Enabling High-Performance Galois-Counter-Mode on
57 * Intel Architecture Processors. October, 2012.
58 * [3] intel-ipsec-mb library, https://github.com/01org/intel-ipsec-mb.git
61 * GF Galois Extension Field GF(2^128) - finite field where elements are
62 * represented as polynomials with coefficients in GF(2) with the
63 * highest degree of 127. Polynomials are represented as 128-bit binary
64 * numbers where each bit represents one coefficient.
65 * e.g. polynomial x^5 + x^3 + x + 1 is represented in binary 101011.
66 * H hash key (128 bit)
67 * POLY irreducible polynomial x^127 + x^7 + x^2 + x + 1
68 * RPOLY irreducible polynomial x^128 + x^127 + x^126 + x^121 + 1
69 * + addition in GF, which equals to XOR operation
70 * * multiplication in GF
72 * GF multiplication consists of 2 steps:
73 * - carry-less multiplication of two 128-bit operands into 256-bit result
74 * - reduction of 256-bit result into 128-bit with modulo POLY
76 * GHash is calculated on 128-bit blocks of data according to the following
78 * GH = (GH + data) * hash_key
80 * To avoid bit-reflection of data, this code uses GF multipication
81 * with reversed polynomial:
82 * a * b * x^-127 mod RPOLY
84 * To improve computation speed table Hi is precomputed with powers of H',
85 * where H' is calculated as H<<1 mod RPOLY.
86 * This allows us to improve performance by deferring reduction. For example
87 * to caclulate ghash of 4 128-bit blocks of data (b0, b1, b2, b3), we can do:
90 * ghash_precompute (H, Hi, 4);
92 * ghash_data_t _gd, *gd = &_gd;
93 * ghash_mul_first (gd, GH ^ b0, Hi[3]);
94 * ghash_mul_next (gd, b1, Hi[2]);
95 * ghash_mul_next (gd, b2, Hi[1]);
96 * ghash_mul_next (gd, b3, Hi[0]);
99 * GH = ghash_final (gd);
101 * Reduction step is split into 3 functions so it can be better interleaved
102 * with other code, (i.e. with AES computation).
108 /* on AVX-512 systems we can save a clock cycle by using ternary logic
109 instruction to calculate a XOR b XOR c */
110 static_always_inline __m128i
111 ghash_xor3 (__m128i a, __m128i b, __m128i c)
113 #if defined (__AVX512F__)
114 return _mm_ternarylogic_epi32 (a, b, c, 0x96);
121 __m128i mid, hi, lo, tmp_lo, tmp_hi;
125 static const __m128i ghash_poly = { 1, 0xC200000000000000 };
126 static const __m128i ghash_poly2 = { 0x1C2000000, 0xC200000000000000 };
128 static_always_inline void
129 ghash_mul_first (ghash_data_t * gd, __m128i a, __m128i b)
132 gd->hi = _mm_clmulepi64_si128 (a, b, 0x11);
134 gd->lo = _mm_clmulepi64_si128 (a, b, 0x00);
135 /* a0 * b1 ^ a1 * b0 */
136 gd->mid = (_mm_clmulepi64_si128 (a, b, 0x01) ^
137 _mm_clmulepi64_si128 (a, b, 0x10));
139 /* set gd->pending to 0 so next invocation of ghash_mul_next(...) knows that
140 there is no pending data in tmp_lo and tmp_hi */
144 static_always_inline void
145 ghash_mul_next (ghash_data_t * gd, __m128i a, __m128i b)
148 __m128i hi = _mm_clmulepi64_si128 (a, b, 0x11);
150 __m128i lo = _mm_clmulepi64_si128 (a, b, 0x00);
152 /* this branch will be optimized out by the compiler, and it allows us to
153 reduce number of XOR operations by using ternary logic */
156 /* there is peding data from previous invocation so we can XOR */
157 gd->hi = ghash_xor3 (gd->hi, gd->tmp_hi, hi);
158 gd->lo = ghash_xor3 (gd->lo, gd->tmp_lo, lo);
163 /* there is no peding data from previous invocation so we postpone XOR */
169 /* gd->mid ^= a0 * b1 ^ a1 * b0 */
170 gd->mid = ghash_xor3 (gd->mid,
171 _mm_clmulepi64_si128 (a, b, 0x01),
172 _mm_clmulepi64_si128 (a, b, 0x10));
175 static_always_inline void
176 ghash_reduce (ghash_data_t * gd)
180 /* Final combination:
181 gd->lo ^= gd->mid << 64
182 gd->hi ^= gd->mid >> 64 */
183 __m128i midl = _mm_slli_si128 (gd->mid, 8);
184 __m128i midr = _mm_srli_si128 (gd->mid, 8);
188 gd->lo = ghash_xor3 (gd->lo, gd->tmp_lo, midl);
189 gd->hi = ghash_xor3 (gd->hi, gd->tmp_hi, midr);
197 r = _mm_clmulepi64_si128 (ghash_poly2, gd->lo, 0x01);
198 gd->lo ^= _mm_slli_si128 (r, 8);
201 static_always_inline void
202 ghash_reduce2 (ghash_data_t * gd)
204 gd->tmp_lo = _mm_clmulepi64_si128 (ghash_poly2, gd->lo, 0x00);
205 gd->tmp_hi = _mm_clmulepi64_si128 (ghash_poly2, gd->lo, 0x10);
208 static_always_inline __m128i
209 ghash_final (ghash_data_t * gd)
211 return ghash_xor3 (gd->hi, _mm_srli_si128 (gd->tmp_lo, 4),
212 _mm_slli_si128 (gd->tmp_hi, 4));
215 static_always_inline __m128i
216 ghash_mul (__m128i a, __m128i b)
218 ghash_data_t _gd, *gd = &_gd;
219 ghash_mul_first (gd, a, b);
222 return ghash_final (gd);
225 static_always_inline void
226 ghash_precompute (__m128i H, __m128i * Hi, int count)
229 /* calcullate H<<1 mod poly from the hash key */
230 r = _mm_srli_epi64 (H, 63);
231 H = _mm_slli_epi64 (H, 1);
232 H |= _mm_slli_si128 (r, 8);
233 r = _mm_srli_si128 (r, 8);
234 r = _mm_shuffle_epi32 (r, 0x24);
236 r = _mm_cmpeq_epi32 (r, (__m128i) (u32x4) {1, 0, 0, 1});
238 Hi[0] = H ^ (r & ghash_poly);
240 /* calculate H^(i + 1) */
241 for (int i = 1; i < count; i++)
242 Hi[i] = ghash_mul (Hi[0], Hi[i - 1]);
245 #endif /* __ghash_h__ */
248 * fd.io coding-style-patch-verification: ON
251 * eval: (c-set-style "gnu")