2 * Copyright 2015-2018 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
12 #include <openssl/crypto.h>
14 #include "internal/poly1305.h"
15 #include "poly1305_local.h"
17 size_t Poly1305_ctx_size(void)
19 return sizeof(struct poly1305_context);
22 /* pick 32-bit unsigned integer in little endian order */
23 static unsigned int U8TOU32(const unsigned char *p)
25 return (((unsigned int)(p[0] & 0xff)) |
26 ((unsigned int)(p[1] & 0xff) << 8) |
27 ((unsigned int)(p[2] & 0xff) << 16) |
28 ((unsigned int)(p[3] & 0xff) << 24));
32 * Implementations can be classified by amount of significant bits in
33 * words making up the multi-precision value, or in other words radix
34 * or base of numerical representation, e.g. base 2^64, base 2^32,
35 * base 2^26. Complementary characteristic is how wide is the result of
36 * multiplication of pair of digits, e.g. it would take 128 bits to
37 * accommodate multiplication result in base 2^64 case. These are used
38 * interchangeably. To describe implementation that is. But interface
39 * is designed to isolate this so that low-level primitives implemented
40 * in assembly can be self-contained/self-coherent.
44 * Even though there is __int128 reference implementation targeting
45 * 64-bit platforms provided below, it's not obvious that it's optimal
46 * choice for every one of them. Depending on instruction set overall
47 * amount of instructions can be comparable to one in __int64
48 * implementation. Amount of multiplication instructions would be lower,
49 * but not necessarily overall. And in out-of-order execution context,
50 * it is the latter that can be crucial...
52 * On related note. Poly1305 author, D. J. Bernstein, discusses and
53 * provides floating-point implementations of the algorithm in question.
54 * It made a lot of sense by the time of introduction, because most
55 * then-modern processors didn't have pipelined integer multiplier.
56 * [Not to mention that some had non-constant timing for integer
57 * multiplications.] Floating-point instructions on the other hand could
58 * be issued every cycle, which allowed to achieve better performance.
59 * Nowadays, with SIMD and/or out-or-order execution, shared or
60 * even emulated FPU, it's more complicated, and floating-point
61 * implementation is not necessarily optimal choice in every situation,
67 typedef unsigned int u32;
70 * poly1305_blocks processes a multiple of POLY1305_BLOCK_SIZE blocks
71 * of |inp| no longer than |len|. Behaviour for |len| not divisible by
72 * block size is unspecified in general case, even though in reference
73 * implementation the trailing chunk is simply ignored. Per algorithm
74 * specification, every input block, complete or last partial, is to be
75 * padded with a bit past most significant byte. The latter kind is then
76 * padded with zeros till block size. This last partial block padding
77 * is caller(*)'s responsibility, and because of this the last partial
78 * block is always processed with separate call with |len| set to
79 * POLY1305_BLOCK_SIZE and |padbit| to 0. In all other cases |padbit|
80 * should be set to 1 to perform implicit padding with 128th bit.
81 * poly1305_blocks does not actually check for this constraint though,
82 * it's caller(*)'s responsibility to comply.
84 * (*) In the context "caller" is not application code, but higher
85 * level Poly1305_* from this very module, so that quirks are
89 poly1305_blocks(void *ctx, const unsigned char *inp, size_t len, u32 padbit);
92 * Type-agnostic "rip-off" from constant_time_locl.h
94 # define CONSTANT_TIME_CARRY(a,b) ( \
95 (a ^ ((a ^ b) | ((a - b) ^ b))) >> (sizeof(a) * 8 - 1) \
98 # if (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16) && \
99 (defined(__SIZEOF_LONG__) && __SIZEOF_LONG__==8)
101 typedef unsigned long u64;
102 typedef __uint128_t u128;
109 /* pick 32-bit unsigned integer in little endian order */
110 static u64 U8TOU64(const unsigned char *p)
112 return (((u64)(p[0] & 0xff)) |
113 ((u64)(p[1] & 0xff) << 8) |
114 ((u64)(p[2] & 0xff) << 16) |
115 ((u64)(p[3] & 0xff) << 24) |
116 ((u64)(p[4] & 0xff) << 32) |
117 ((u64)(p[5] & 0xff) << 40) |
118 ((u64)(p[6] & 0xff) << 48) |
119 ((u64)(p[7] & 0xff) << 56));
122 /* store a 32-bit unsigned integer in little endian */
123 static void U64TO8(unsigned char *p, u64 v)
125 p[0] = (unsigned char)((v) & 0xff);
126 p[1] = (unsigned char)((v >> 8) & 0xff);
127 p[2] = (unsigned char)((v >> 16) & 0xff);
128 p[3] = (unsigned char)((v >> 24) & 0xff);
129 p[4] = (unsigned char)((v >> 32) & 0xff);
130 p[5] = (unsigned char)((v >> 40) & 0xff);
131 p[6] = (unsigned char)((v >> 48) & 0xff);
132 p[7] = (unsigned char)((v >> 56) & 0xff);
135 static void poly1305_init(void *ctx, const unsigned char key[16])
137 poly1305_internal *st = (poly1305_internal *) ctx;
144 /* r &= 0xffffffc0ffffffc0ffffffc0fffffff */
145 st->r[0] = U8TOU64(&key[0]) & 0x0ffffffc0fffffff;
146 st->r[1] = U8TOU64(&key[8]) & 0x0ffffffc0ffffffc;
150 poly1305_blocks(void *ctx, const unsigned char *inp, size_t len, u32 padbit)
152 poly1305_internal *st = (poly1305_internal *)ctx;
167 while (len >= POLY1305_BLOCK_SIZE) {
169 h0 = (u64)(d0 = (u128)h0 + U8TOU64(inp + 0));
170 h1 = (u64)(d1 = (u128)h1 + (d0 >> 64) + U8TOU64(inp + 8));
172 * padbit can be zero only when original len was
173 * POLY1306_BLOCK_SIZE, but we don't check
175 h2 += (u64)(d1 >> 64) + padbit;
177 /* h *= r "%" p, where "%" stands for "partial remainder" */
178 d0 = ((u128)h0 * r0) +
180 d1 = ((u128)h0 * r1) +
185 /* last reduction step: */
186 /* a) h2:h0 = h2<<128 + d1<<64 + d0 */
188 h1 = (u64)(d1 += d0 >> 64);
189 h2 += (u64)(d1 >> 64);
190 /* b) (h2:h0 += (h2:h0>>130) * 5) %= 2^130 */
191 c = (h2 >> 2) + (h2 & ~3UL);
194 h1 += (c = CONSTANT_TIME_CARRY(h0,c));
195 h2 += CONSTANT_TIME_CARRY(h1,c);
197 * Occasional overflows to 3rd bit of h2 are taken care of
198 * "naturally". If after this point we end up at the top of
199 * this loop, then the overflow bit will be accounted for
200 * in next iteration. If we end up in poly1305_emit, then
201 * comparison to modulus below will still count as "carry
202 * into 131st bit", so that properly reduced value will be
203 * picked in conditional move.
206 inp += POLY1305_BLOCK_SIZE;
207 len -= POLY1305_BLOCK_SIZE;
215 static void poly1305_emit(void *ctx, unsigned char mac[16],
218 poly1305_internal *st = (poly1305_internal *) ctx;
228 /* compare to modulus by computing h + -p */
229 g0 = (u64)(t = (u128)h0 + 5);
230 g1 = (u64)(t = (u128)h1 + (t >> 64));
231 g2 = h2 + (u64)(t >> 64);
233 /* if there was carry into 131st bit, h1:h0 = g1:g0 */
234 mask = 0 - (g2 >> 2);
238 h0 = (h0 & mask) | g0;
239 h1 = (h1 & mask) | g1;
241 /* mac = (h + nonce) % (2^128) */
242 h0 = (u64)(t = (u128)h0 + nonce[0] + ((u64)nonce[1]<<32));
243 h1 = (u64)(t = (u128)h1 + nonce[2] + ((u64)nonce[3]<<32) + (t >> 64));
251 # if defined(_WIN32) && !defined(__MINGW32__)
252 typedef unsigned __int64 u64;
253 # elif defined(__arch64__)
254 typedef unsigned long u64;
256 typedef unsigned long long u64;
264 /* store a 32-bit unsigned integer in little endian */
265 static void U32TO8(unsigned char *p, unsigned int v)
267 p[0] = (unsigned char)((v) & 0xff);
268 p[1] = (unsigned char)((v >> 8) & 0xff);
269 p[2] = (unsigned char)((v >> 16) & 0xff);
270 p[3] = (unsigned char)((v >> 24) & 0xff);
273 static void poly1305_init(void *ctx, const unsigned char key[16])
275 poly1305_internal *st = (poly1305_internal *) ctx;
284 /* r &= 0xffffffc0ffffffc0ffffffc0fffffff */
285 st->r[0] = U8TOU32(&key[0]) & 0x0fffffff;
286 st->r[1] = U8TOU32(&key[4]) & 0x0ffffffc;
287 st->r[2] = U8TOU32(&key[8]) & 0x0ffffffc;
288 st->r[3] = U8TOU32(&key[12]) & 0x0ffffffc;
292 poly1305_blocks(void *ctx, const unsigned char *inp, size_t len, u32 padbit)
294 poly1305_internal *st = (poly1305_internal *)ctx;
297 u32 h0, h1, h2, h3, h4, c;
315 while (len >= POLY1305_BLOCK_SIZE) {
317 h0 = (u32)(d0 = (u64)h0 + U8TOU32(inp + 0));
318 h1 = (u32)(d1 = (u64)h1 + (d0 >> 32) + U8TOU32(inp + 4));
319 h2 = (u32)(d2 = (u64)h2 + (d1 >> 32) + U8TOU32(inp + 8));
320 h3 = (u32)(d3 = (u64)h3 + (d2 >> 32) + U8TOU32(inp + 12));
321 h4 += (u32)(d3 >> 32) + padbit;
323 /* h *= r "%" p, where "%" stands for "partial remainder" */
324 d0 = ((u64)h0 * r0) +
328 d1 = ((u64)h0 * r1) +
333 d2 = ((u64)h0 * r2) +
338 d3 = ((u64)h0 * r3) +
345 /* last reduction step: */
346 /* a) h4:h0 = h4<<128 + d3<<96 + d2<<64 + d1<<32 + d0 */
348 h1 = (u32)(d1 += d0 >> 32);
349 h2 = (u32)(d2 += d1 >> 32);
350 h3 = (u32)(d3 += d2 >> 32);
351 h4 += (u32)(d3 >> 32);
352 /* b) (h4:h0 += (h4:h0>>130) * 5) %= 2^130 */
353 c = (h4 >> 2) + (h4 & ~3U);
356 h1 += (c = CONSTANT_TIME_CARRY(h0,c));
357 h2 += (c = CONSTANT_TIME_CARRY(h1,c));
358 h3 += (c = CONSTANT_TIME_CARRY(h2,c));
359 h4 += CONSTANT_TIME_CARRY(h3,c);
361 * Occasional overflows to 3rd bit of h4 are taken care of
362 * "naturally". If after this point we end up at the top of
363 * this loop, then the overflow bit will be accounted for
364 * in next iteration. If we end up in poly1305_emit, then
365 * comparison to modulus below will still count as "carry
366 * into 131st bit", so that properly reduced value will be
367 * picked in conditional move.
370 inp += POLY1305_BLOCK_SIZE;
371 len -= POLY1305_BLOCK_SIZE;
381 static void poly1305_emit(void *ctx, unsigned char mac[16],
384 poly1305_internal *st = (poly1305_internal *) ctx;
385 u32 h0, h1, h2, h3, h4;
386 u32 g0, g1, g2, g3, g4;
396 /* compare to modulus by computing h + -p */
397 g0 = (u32)(t = (u64)h0 + 5);
398 g1 = (u32)(t = (u64)h1 + (t >> 32));
399 g2 = (u32)(t = (u64)h2 + (t >> 32));
400 g3 = (u32)(t = (u64)h3 + (t >> 32));
401 g4 = h4 + (u32)(t >> 32);
403 /* if there was carry into 131st bit, h3:h0 = g3:g0 */
404 mask = 0 - (g4 >> 2);
410 h0 = (h0 & mask) | g0;
411 h1 = (h1 & mask) | g1;
412 h2 = (h2 & mask) | g2;
413 h3 = (h3 & mask) | g3;
415 /* mac = (h + nonce) % (2^128) */
416 h0 = (u32)(t = (u64)h0 + nonce[0]);
417 h1 = (u32)(t = (u64)h1 + (t >> 32) + nonce[1]);
418 h2 = (u32)(t = (u64)h2 + (t >> 32) + nonce[2]);
419 h3 = (u32)(t = (u64)h3 + (t >> 32) + nonce[3]);
424 U32TO8(mac + 12, h3);
428 int poly1305_init(void *ctx, const unsigned char key[16], void *func);
429 void poly1305_blocks(void *ctx, const unsigned char *inp, size_t len,
430 unsigned int padbit);
431 void poly1305_emit(void *ctx, unsigned char mac[16],
432 const unsigned int nonce[4]);
435 void Poly1305_Init(POLY1305 *ctx, const unsigned char key[32])
437 ctx->nonce[0] = U8TOU32(&key[16]);
438 ctx->nonce[1] = U8TOU32(&key[20]);
439 ctx->nonce[2] = U8TOU32(&key[24]);
440 ctx->nonce[3] = U8TOU32(&key[28]);
443 poly1305_init(ctx->opaque, key);
446 * Unlike reference poly1305_init assembly counterpart is expected
447 * to return a value: non-zero if it initializes ctx->func, and zero
448 * otherwise. Latter is to simplify assembly in cases when there no
449 * multiple code paths to switch between.
451 if (!poly1305_init(ctx->opaque, key, &ctx->func)) {
452 ctx->func.blocks = poly1305_blocks;
453 ctx->func.emit = poly1305_emit;
463 * This "eclipses" poly1305_blocks and poly1305_emit, but it's
464 * conscious choice imposed by -Wshadow compiler warnings.
466 # define poly1305_blocks (*poly1305_blocks_p)
467 # define poly1305_emit (*poly1305_emit_p)
470 void Poly1305_Update(POLY1305 *ctx, const unsigned char *inp, size_t len)
474 * As documented, poly1305_blocks is never called with input
475 * longer than single block and padbit argument set to 0. This
476 * property is fluently used in assembly modules to optimize
477 * padbit handling on loop boundary.
479 poly1305_blocks_f poly1305_blocks_p = ctx->func.blocks;
483 if ((num = ctx->num)) {
484 rem = POLY1305_BLOCK_SIZE - num;
486 memcpy(ctx->data + num, inp, rem);
487 poly1305_blocks(ctx->opaque, ctx->data, POLY1305_BLOCK_SIZE, 1);
491 /* Still not enough data to process a block. */
492 memcpy(ctx->data + num, inp, len);
493 ctx->num = num + len;
498 rem = len % POLY1305_BLOCK_SIZE;
501 if (len >= POLY1305_BLOCK_SIZE) {
502 poly1305_blocks(ctx->opaque, inp, len, 1);
507 memcpy(ctx->data, inp, rem);
512 void Poly1305_Final(POLY1305 *ctx, unsigned char mac[16])
515 poly1305_blocks_f poly1305_blocks_p = ctx->func.blocks;
516 poly1305_emit_f poly1305_emit_p = ctx->func.emit;
520 if ((num = ctx->num)) {
521 ctx->data[num++] = 1; /* pad bit */
522 while (num < POLY1305_BLOCK_SIZE)
523 ctx->data[num++] = 0;
524 poly1305_blocks(ctx->opaque, ctx->data, POLY1305_BLOCK_SIZE, 0);
527 poly1305_emit(ctx->opaque, mac, ctx->nonce);
529 /* zero out the state */
530 OPENSSL_cleanse(ctx, sizeof(*ctx));