2 * Copyright 2015-2021 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the Apache License 2.0 (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 "crypto/poly1305.h"
16 size_t Poly1305_ctx_size(void)
18 return sizeof(struct poly1305_context);
21 /* pick 32-bit unsigned integer in little endian order */
22 static unsigned int U8TOU32(const unsigned char *p)
24 return (((unsigned int)(p[0] & 0xff)) |
25 ((unsigned int)(p[1] & 0xff) << 8) |
26 ((unsigned int)(p[2] & 0xff) << 16) |
27 ((unsigned int)(p[3] & 0xff) << 24));
31 * Implementations can be classified by amount of significant bits in
32 * words making up the multi-precision value, or in other words radix
33 * or base of numerical representation, e.g. base 2^64, base 2^32,
34 * base 2^26. Complementary characteristic is how wide is the result of
35 * multiplication of pair of digits, e.g. it would take 128 bits to
36 * accommodate multiplication result in base 2^64 case. These are used
37 * interchangeably. To describe implementation that is. But interface
38 * is designed to isolate this so that low-level primitives implemented
39 * in assembly can be self-contained/self-coherent.
43 * Even though there is __int128 reference implementation targeting
44 * 64-bit platforms provided below, it's not obvious that it's optimal
45 * choice for every one of them. Depending on instruction set overall
46 * amount of instructions can be comparable to one in __int64
47 * implementation. Amount of multiplication instructions would be lower,
48 * but not necessarily overall. And in out-of-order execution context,
49 * it is the latter that can be crucial...
51 * On related note. Poly1305 author, D. J. Bernstein, discusses and
52 * provides floating-point implementations of the algorithm in question.
53 * It made a lot of sense by the time of introduction, because most
54 * then-modern processors didn't have pipelined integer multiplier.
55 * [Not to mention that some had non-constant timing for integer
56 * multiplications.] Floating-point instructions on the other hand could
57 * be issued every cycle, which allowed to achieve better performance.
58 * Nowadays, with SIMD and/or out-or-order execution, shared or
59 * even emulated FPU, it's more complicated, and floating-point
60 * implementation is not necessarily optimal choice in every situation,
66 typedef unsigned int u32;
69 * poly1305_blocks processes a multiple of POLY1305_BLOCK_SIZE blocks
70 * of |inp| no longer than |len|. Behaviour for |len| not divisible by
71 * block size is unspecified in general case, even though in reference
72 * implementation the trailing chunk is simply ignored. Per algorithm
73 * specification, every input block, complete or last partial, is to be
74 * padded with a bit past most significant byte. The latter kind is then
75 * padded with zeros till block size. This last partial block padding
76 * is caller(*)'s responsibility, and because of this the last partial
77 * block is always processed with separate call with |len| set to
78 * POLY1305_BLOCK_SIZE and |padbit| to 0. In all other cases |padbit|
79 * should be set to 1 to perform implicit padding with 128th bit.
80 * poly1305_blocks does not actually check for this constraint though,
81 * it's caller(*)'s responsibility to comply.
83 * (*) In the context "caller" is not application code, but higher
84 * level Poly1305_* from this very module, so that quirks are
88 poly1305_blocks(void *ctx, const unsigned char *inp, size_t len, u32 padbit);
91 * Type-agnostic "rip-off" from constant_time.h
93 # define CONSTANT_TIME_CARRY(a,b) ( \
94 (a ^ ((a ^ b) | ((a - b) ^ b))) >> (sizeof(a) * 8 - 1) \
97 # if defined(INT64_MAX) && defined(INT128_MAX)
99 typedef unsigned long u64;
100 typedef uint128_t u128;
107 /* pick 32-bit unsigned integer in little endian order */
108 static u64 U8TOU64(const unsigned char *p)
110 return (((u64)(p[0] & 0xff)) |
111 ((u64)(p[1] & 0xff) << 8) |
112 ((u64)(p[2] & 0xff) << 16) |
113 ((u64)(p[3] & 0xff) << 24) |
114 ((u64)(p[4] & 0xff) << 32) |
115 ((u64)(p[5] & 0xff) << 40) |
116 ((u64)(p[6] & 0xff) << 48) |
117 ((u64)(p[7] & 0xff) << 56));
120 /* store a 32-bit unsigned integer in little endian */
121 static void U64TO8(unsigned char *p, u64 v)
123 p[0] = (unsigned char)((v) & 0xff);
124 p[1] = (unsigned char)((v >> 8) & 0xff);
125 p[2] = (unsigned char)((v >> 16) & 0xff);
126 p[3] = (unsigned char)((v >> 24) & 0xff);
127 p[4] = (unsigned char)((v >> 32) & 0xff);
128 p[5] = (unsigned char)((v >> 40) & 0xff);
129 p[6] = (unsigned char)((v >> 48) & 0xff);
130 p[7] = (unsigned char)((v >> 56) & 0xff);
133 static void poly1305_init(void *ctx, const unsigned char key[16])
135 poly1305_internal *st = (poly1305_internal *) ctx;
142 /* r &= 0xffffffc0ffffffc0ffffffc0fffffff */
143 st->r[0] = U8TOU64(&key[0]) & 0x0ffffffc0fffffff;
144 st->r[1] = U8TOU64(&key[8]) & 0x0ffffffc0ffffffc;
148 poly1305_blocks(void *ctx, const unsigned char *inp, size_t len, u32 padbit)
150 poly1305_internal *st = (poly1305_internal *)ctx;
165 while (len >= POLY1305_BLOCK_SIZE) {
167 h0 = (u64)(d0 = (u128)h0 + U8TOU64(inp + 0));
168 h1 = (u64)(d1 = (u128)h1 + (d0 >> 64) + U8TOU64(inp + 8));
170 * padbit can be zero only when original len was
171 * POLY1305_BLOCK_SIZE, but we don't check
173 h2 += (u64)(d1 >> 64) + padbit;
175 /* h *= r "%" p, where "%" stands for "partial remainder" */
176 d0 = ((u128)h0 * r0) +
178 d1 = ((u128)h0 * r1) +
183 /* last reduction step: */
184 /* a) h2:h0 = h2<<128 + d1<<64 + d0 */
186 h1 = (u64)(d1 += d0 >> 64);
187 h2 += (u64)(d1 >> 64);
188 /* b) (h2:h0 += (h2:h0>>130) * 5) %= 2^130 */
189 c = (h2 >> 2) + (h2 & ~3UL);
192 h1 += (c = CONSTANT_TIME_CARRY(h0,c));
193 h2 += CONSTANT_TIME_CARRY(h1,c);
195 * Occasional overflows to 3rd bit of h2 are taken care of
196 * "naturally". If after this point we end up at the top of
197 * this loop, then the overflow bit will be accounted for
198 * in next iteration. If we end up in poly1305_emit, then
199 * comparison to modulus below will still count as "carry
200 * into 131st bit", so that properly reduced value will be
201 * picked in conditional move.
204 inp += POLY1305_BLOCK_SIZE;
205 len -= POLY1305_BLOCK_SIZE;
213 static void poly1305_emit(void *ctx, unsigned char mac[16],
216 poly1305_internal *st = (poly1305_internal *) ctx;
226 /* compare to modulus by computing h + -p */
227 g0 = (u64)(t = (u128)h0 + 5);
228 g1 = (u64)(t = (u128)h1 + (t >> 64));
229 g2 = h2 + (u64)(t >> 64);
231 /* if there was carry into 131st bit, h1:h0 = g1:g0 */
232 mask = 0 - (g2 >> 2);
236 h0 = (h0 & mask) | g0;
237 h1 = (h1 & mask) | g1;
239 /* mac = (h + nonce) % (2^128) */
240 h0 = (u64)(t = (u128)h0 + nonce[0] + ((u64)nonce[1]<<32));
241 h1 = (u64)(t = (u128)h1 + nonce[2] + ((u64)nonce[3]<<32) + (t >> 64));
249 # if defined(_WIN32) && !defined(__MINGW32__)
250 typedef unsigned __int64 u64;
251 # elif defined(__arch64__)
252 typedef unsigned long u64;
254 typedef unsigned long long u64;
262 /* store a 32-bit unsigned integer in little endian */
263 static void U32TO8(unsigned char *p, unsigned int v)
265 p[0] = (unsigned char)((v) & 0xff);
266 p[1] = (unsigned char)((v >> 8) & 0xff);
267 p[2] = (unsigned char)((v >> 16) & 0xff);
268 p[3] = (unsigned char)((v >> 24) & 0xff);
271 static void poly1305_init(void *ctx, const unsigned char key[16])
273 poly1305_internal *st = (poly1305_internal *) ctx;
282 /* r &= 0xffffffc0ffffffc0ffffffc0fffffff */
283 st->r[0] = U8TOU32(&key[0]) & 0x0fffffff;
284 st->r[1] = U8TOU32(&key[4]) & 0x0ffffffc;
285 st->r[2] = U8TOU32(&key[8]) & 0x0ffffffc;
286 st->r[3] = U8TOU32(&key[12]) & 0x0ffffffc;
290 poly1305_blocks(void *ctx, const unsigned char *inp, size_t len, u32 padbit)
292 poly1305_internal *st = (poly1305_internal *)ctx;
295 u32 h0, h1, h2, h3, h4, c;
313 while (len >= POLY1305_BLOCK_SIZE) {
315 h0 = (u32)(d0 = (u64)h0 + U8TOU32(inp + 0));
316 h1 = (u32)(d1 = (u64)h1 + (d0 >> 32) + U8TOU32(inp + 4));
317 h2 = (u32)(d2 = (u64)h2 + (d1 >> 32) + U8TOU32(inp + 8));
318 h3 = (u32)(d3 = (u64)h3 + (d2 >> 32) + U8TOU32(inp + 12));
319 h4 += (u32)(d3 >> 32) + padbit;
321 /* h *= r "%" p, where "%" stands for "partial remainder" */
322 d0 = ((u64)h0 * r0) +
326 d1 = ((u64)h0 * r1) +
331 d2 = ((u64)h0 * r2) +
336 d3 = ((u64)h0 * r3) +
343 /* last reduction step: */
344 /* a) h4:h0 = h4<<128 + d3<<96 + d2<<64 + d1<<32 + d0 */
346 h1 = (u32)(d1 += d0 >> 32);
347 h2 = (u32)(d2 += d1 >> 32);
348 h3 = (u32)(d3 += d2 >> 32);
349 h4 += (u32)(d3 >> 32);
350 /* b) (h4:h0 += (h4:h0>>130) * 5) %= 2^130 */
351 c = (h4 >> 2) + (h4 & ~3U);
354 h1 += (c = CONSTANT_TIME_CARRY(h0,c));
355 h2 += (c = CONSTANT_TIME_CARRY(h1,c));
356 h3 += (c = CONSTANT_TIME_CARRY(h2,c));
357 h4 += CONSTANT_TIME_CARRY(h3,c);
359 * Occasional overflows to 3rd bit of h4 are taken care of
360 * "naturally". If after this point we end up at the top of
361 * this loop, then the overflow bit will be accounted for
362 * in next iteration. If we end up in poly1305_emit, then
363 * comparison to modulus below will still count as "carry
364 * into 131st bit", so that properly reduced value will be
365 * picked in conditional move.
368 inp += POLY1305_BLOCK_SIZE;
369 len -= POLY1305_BLOCK_SIZE;
379 static void poly1305_emit(void *ctx, unsigned char mac[16],
382 poly1305_internal *st = (poly1305_internal *) ctx;
383 u32 h0, h1, h2, h3, h4;
384 u32 g0, g1, g2, g3, g4;
394 /* compare to modulus by computing h + -p */
395 g0 = (u32)(t = (u64)h0 + 5);
396 g1 = (u32)(t = (u64)h1 + (t >> 32));
397 g2 = (u32)(t = (u64)h2 + (t >> 32));
398 g3 = (u32)(t = (u64)h3 + (t >> 32));
399 g4 = h4 + (u32)(t >> 32);
401 /* if there was carry into 131st bit, h3:h0 = g3:g0 */
402 mask = 0 - (g4 >> 2);
408 h0 = (h0 & mask) | g0;
409 h1 = (h1 & mask) | g1;
410 h2 = (h2 & mask) | g2;
411 h3 = (h3 & mask) | g3;
413 /* mac = (h + nonce) % (2^128) */
414 h0 = (u32)(t = (u64)h0 + nonce[0]);
415 h1 = (u32)(t = (u64)h1 + (t >> 32) + nonce[1]);
416 h2 = (u32)(t = (u64)h2 + (t >> 32) + nonce[2]);
417 h3 = (u32)(t = (u64)h3 + (t >> 32) + nonce[3]);
422 U32TO8(mac + 12, h3);
426 int poly1305_init(void *ctx, const unsigned char key[16], void *func);
427 void poly1305_blocks(void *ctx, const unsigned char *inp, size_t len,
428 unsigned int padbit);
429 void poly1305_emit(void *ctx, unsigned char mac[16],
430 const unsigned int nonce[4]);
433 void Poly1305_Init(POLY1305 *ctx, const unsigned char key[32])
435 ctx->nonce[0] = U8TOU32(&key[16]);
436 ctx->nonce[1] = U8TOU32(&key[20]);
437 ctx->nonce[2] = U8TOU32(&key[24]);
438 ctx->nonce[3] = U8TOU32(&key[28]);
441 poly1305_init(ctx->opaque, key);
444 * Unlike reference poly1305_init assembly counterpart is expected
445 * to return a value: non-zero if it initializes ctx->func, and zero
446 * otherwise. Latter is to simplify assembly in cases when there no
447 * multiple code paths to switch between.
449 if (!poly1305_init(ctx->opaque, key, &ctx->func)) {
450 ctx->func.blocks = poly1305_blocks;
451 ctx->func.emit = poly1305_emit;
461 * This "eclipses" poly1305_blocks and poly1305_emit, but it's
462 * conscious choice imposed by -Wshadow compiler warnings.
464 # define poly1305_blocks (*poly1305_blocks_p)
465 # define poly1305_emit (*poly1305_emit_p)
468 void Poly1305_Update(POLY1305 *ctx, const unsigned char *inp, size_t len)
472 * As documented, poly1305_blocks is never called with input
473 * longer than single block and padbit argument set to 0. This
474 * property is fluently used in assembly modules to optimize
475 * padbit handling on loop boundary.
477 poly1305_blocks_f poly1305_blocks_p = ctx->func.blocks;
481 if ((num = ctx->num)) {
482 rem = POLY1305_BLOCK_SIZE - num;
484 memcpy(ctx->data + num, inp, rem);
485 poly1305_blocks(ctx->opaque, ctx->data, POLY1305_BLOCK_SIZE, 1);
489 /* Still not enough data to process a block. */
490 memcpy(ctx->data + num, inp, len);
491 ctx->num = num + len;
496 rem = len % POLY1305_BLOCK_SIZE;
499 if (len >= POLY1305_BLOCK_SIZE) {
500 poly1305_blocks(ctx->opaque, inp, len, 1);
505 memcpy(ctx->data, inp, rem);
510 void Poly1305_Final(POLY1305 *ctx, unsigned char mac[16])
513 poly1305_blocks_f poly1305_blocks_p = ctx->func.blocks;
514 poly1305_emit_f poly1305_emit_p = ctx->func.emit;
518 if ((num = ctx->num)) {
519 ctx->data[num++] = 1; /* pad bit */
520 while (num < POLY1305_BLOCK_SIZE)
521 ctx->data[num++] = 0;
522 poly1305_blocks(ctx->opaque, ctx->data, POLY1305_BLOCK_SIZE, 0);
525 poly1305_emit(ctx->opaque, mac, ctx->nonce);
527 /* zero out the state */
528 OPENSSL_cleanse(ctx, sizeof(*ctx));