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/*
* Copyright 2015-2018 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the Apache License 2.0 (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
#include <stdlib.h>
#include <string.h>
#include <openssl/crypto.h>
#include "crypto/poly1305.h"
size_t Poly1305_ctx_size(void)
{
return sizeof(struct poly1305_context);
}
/* pick 32-bit unsigned integer in little endian order */
static unsigned int U8TOU32(const unsigned char *p)
{
return (((unsigned int)(p[0] & 0xff)) |
((unsigned int)(p[1] & 0xff) << 8) |
((unsigned int)(p[2] & 0xff) << 16) |
((unsigned int)(p[3] & 0xff) << 24));
}
/*
* Implementations can be classified by amount of significant bits in
* words making up the multi-precision value, or in other words radix
* or base of numerical representation, e.g. base 2^64, base 2^32,
* base 2^26. Complementary characteristic is how wide is the result of
* multiplication of pair of digits, e.g. it would take 128 bits to
* accommodate multiplication result in base 2^64 case. These are used
* interchangeably. To describe implementation that is. But interface
* is designed to isolate this so that low-level primitives implemented
* in assembly can be self-contained/self-coherent.
*/
#ifndef POLY1305_ASM
/*
* Even though there is __int128 reference implementation targeting
* 64-bit platforms provided below, it's not obvious that it's optimal
* choice for every one of them. Depending on instruction set overall
* amount of instructions can be comparable to one in __int64
* implementation. Amount of multiplication instructions would be lower,
* but not necessarily overall. And in out-of-order execution context,
* it is the latter that can be crucial...
*
* On related note. Poly1305 author, D. J. Bernstein, discusses and
* provides floating-point implementations of the algorithm in question.
* It made a lot of sense by the time of introduction, because most
* then-modern processors didn't have pipelined integer multiplier.
* [Not to mention that some had non-constant timing for integer
* multiplications.] Floating-point instructions on the other hand could
* be issued every cycle, which allowed to achieve better performance.
* Nowadays, with SIMD and/or out-or-order execution, shared or
* even emulated FPU, it's more complicated, and floating-point
* implementation is not necessarily optimal choice in every situation,
* rather contrary...
*
* <appro@openssl.org>
*/
typedef unsigned int u32;
/*
* poly1305_blocks processes a multiple of POLY1305_BLOCK_SIZE blocks
* of |inp| no longer than |len|. Behaviour for |len| not divisible by
* block size is unspecified in general case, even though in reference
* implementation the trailing chunk is simply ignored. Per algorithm
* specification, every input block, complete or last partial, is to be
* padded with a bit past most significant byte. The latter kind is then
* padded with zeros till block size. This last partial block padding
* is caller(*)'s responsibility, and because of this the last partial
* block is always processed with separate call with |len| set to
* POLY1305_BLOCK_SIZE and |padbit| to 0. In all other cases |padbit|
* should be set to 1 to perform implicit padding with 128th bit.
* poly1305_blocks does not actually check for this constraint though,
* it's caller(*)'s responsibility to comply.
*
* (*) In the context "caller" is not application code, but higher
* level Poly1305_* from this very module, so that quirks are
* handled locally.
*/
static void
poly1305_blocks(void *ctx, const unsigned char *inp, size_t len, u32 padbit);
/*
* Type-agnostic "rip-off" from constant_time.h
*/
# define CONSTANT_TIME_CARRY(a,b) ( \
(a ^ ((a ^ b) | ((a - b) ^ b))) >> (sizeof(a) * 8 - 1) \
)
# if (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16) && \
(defined(__SIZEOF_LONG__) && __SIZEOF_LONG__==8)
typedef unsigned long u64;
typedef __uint128_t u128;
typedef struct {
u64 h[3];
u64 r[2];
} poly1305_internal;
/* pick 32-bit unsigned integer in little endian order */
static u64 U8TOU64(const unsigned char *p)
{
return (((u64)(p[0] & 0xff)) |
((u64)(p[1] & 0xff) << 8) |
((u64)(p[2] & 0xff) << 16) |
((u64)(p[3] & 0xff) << 24) |
((u64)(p[4] & 0xff) << 32) |
((u64)(p[5] & 0xff) << 40) |
((u64)(p[6] & 0xff) << 48) |
((u64)(p[7] & 0xff) << 56));
}
/* store a 32-bit unsigned integer in little endian */
static void U64TO8(unsigned char *p, u64 v)
{
p[0] = (unsigned char)((v) & 0xff);
p[1] = (unsigned char)((v >> 8) & 0xff);
p[2] = (unsigned char)((v >> 16) & 0xff);
p[3] = (unsigned char)((v >> 24) & 0xff);
p[4] = (unsigned char)((v >> 32) & 0xff);
p[5] = (unsigned char)((v >> 40) & 0xff);
p[6] = (unsigned char)((v >> 48) & 0xff);
p[7] = (unsigned char)((v >> 56) & 0xff);
}
static void poly1305_init(void *ctx, const unsigned char key[16])
{
poly1305_internal *st = (poly1305_internal *) ctx;
/* h = 0 */
st->h[0] = 0;
st->h[1] = 0;
st->h[2] = 0;
/* r &= 0xffffffc0ffffffc0ffffffc0fffffff */
st->r[0] = U8TOU64(&key[0]) & 0x0ffffffc0fffffff;
st->r[1] = U8TOU64(&key[8]) & 0x0ffffffc0ffffffc;
}
static void
poly1305_blocks(void *ctx, const unsigned char *inp, size_t len, u32 padbit)
{
poly1305_internal *st = (poly1305_internal *)ctx;
u64 r0, r1;
u64 s1;
u64 h0, h1, h2, c;
u128 d0, d1;
r0 = st->r[0];
r1 = st->r[1];
s1 = r1 + (r1 >> 2);
h0 = st->h[0];
h1 = st->h[1];
h2 = st->h[2];
while (len >= POLY1305_BLOCK_SIZE) {
/* h += m[i] */
h0 = (u64)(d0 = (u128)h0 + U8TOU64(inp + 0));
h1 = (u64)(d1 = (u128)h1 + (d0 >> 64) + U8TOU64(inp + 8));
/*
* padbit can be zero only when original len was
* POLY1306_BLOCK_SIZE, but we don't check
*/
h2 += (u64)(d1 >> 64) + padbit;
/* h *= r "%" p, where "%" stands for "partial remainder" */
d0 = ((u128)h0 * r0) +
((u128)h1 * s1);
d1 = ((u128)h0 * r1) +
((u128)h1 * r0) +
(h2 * s1);
h2 = (h2 * r0);
/* last reduction step: */
/* a) h2:h0 = h2<<128 + d1<<64 + d0 */
h0 = (u64)d0;
h1 = (u64)(d1 += d0 >> 64);
h2 += (u64)(d1 >> 64);
/* b) (h2:h0 += (h2:h0>>130) * 5) %= 2^130 */
c = (h2 >> 2) + (h2 & ~3UL);
h2 &= 3;
h0 += c;
h1 += (c = CONSTANT_TIME_CARRY(h0,c));
h2 += CONSTANT_TIME_CARRY(h1,c);
/*
* Occasional overflows to 3rd bit of h2 are taken care of
* "naturally". If after this point we end up at the top of
* this loop, then the overflow bit will be accounted for
* in next iteration. If we end up in poly1305_emit, then
* comparison to modulus below will still count as "carry
* into 131st bit", so that properly reduced value will be
* picked in conditional move.
*/
inp += POLY1305_BLOCK_SIZE;
len -= POLY1305_BLOCK_SIZE;
}
st->h[0] = h0;
st->h[1] = h1;
st->h[2] = h2;
}
static void poly1305_emit(void *ctx, unsigned char mac[16],
const u32 nonce[4])
{
poly1305_internal *st = (poly1305_internal *) ctx;
u64 h0, h1, h2;
u64 g0, g1, g2;
u128 t;
u64 mask;
h0 = st->h[0];
h1 = st->h[1];
h2 = st->h[2];
/* compare to modulus by computing h + -p */
g0 = (u64)(t = (u128)h0 + 5);
g1 = (u64)(t = (u128)h1 + (t >> 64));
g2 = h2 + (u64)(t >> 64);
/* if there was carry into 131st bit, h1:h0 = g1:g0 */
mask = 0 - (g2 >> 2);
g0 &= mask;
g1 &= mask;
mask = ~mask;
h0 = (h0 & mask) | g0;
h1 = (h1 & mask) | g1;
/* mac = (h + nonce) % (2^128) */
h0 = (u64)(t = (u128)h0 + nonce[0] + ((u64)nonce[1]<<32));
h1 = (u64)(t = (u128)h1 + nonce[2] + ((u64)nonce[3]<<32) + (t >> 64));
U64TO8(mac + 0, h0);
U64TO8(mac + 8, h1);
}
# else
# if defined(_WIN32) && !defined(__MINGW32__)
typedef unsigned __int64 u64;
# elif defined(__arch64__)
typedef unsigned long u64;
# else
typedef unsigned long long u64;
# endif
typedef struct {
u32 h[5];
u32 r[4];
} poly1305_internal;
/* store a 32-bit unsigned integer in little endian */
static void U32TO8(unsigned char *p, unsigned int v)
{
p[0] = (unsigned char)((v) & 0xff);
p[1] = (unsigned char)((v >> 8) & 0xff);
p[2] = (unsigned char)((v >> 16) & 0xff);
p[3] = (unsigned char)((v >> 24) & 0xff);
}
static void poly1305_init(void *ctx, const unsigned char key[16])
{
poly1305_internal *st = (poly1305_internal *) ctx;
/* h = 0 */
st->h[0] = 0;
st->h[1] = 0;
st->h[2] = 0;
st->h[3] = 0;
st->h[4] = 0;
/* r &= 0xffffffc0ffffffc0ffffffc0fffffff */
st->r[0] = U8TOU32(&key[0]) & 0x0fffffff;
st->r[1] = U8TOU32(&key[4]) & 0x0ffffffc;
st->r[2] = U8TOU32(&key[8]) & 0x0ffffffc;
st->r[3] = U8TOU32(&key[12]) & 0x0ffffffc;
}
static void
poly1305_blocks(void *ctx, const unsigned char *inp, size_t len, u32 padbit)
{
poly1305_internal *st = (poly1305_internal *)ctx;
u32 r0, r1, r2, r3;
u32 s1, s2, s3;
u32 h0, h1, h2, h3, h4, c;
u64 d0, d1, d2, d3;
r0 = st->r[0];
r1 = st->r[1];
r2 = st->r[2];
r3 = st->r[3];
s1 = r1 + (r1 >> 2);
s2 = r2 + (r2 >> 2);
s3 = r3 + (r3 >> 2);
h0 = st->h[0];
h1 = st->h[1];
h2 = st->h[2];
h3 = st->h[3];
h4 = st->h[4];
while (len >= POLY1305_BLOCK_SIZE) {
/* h += m[i] */
h0 = (u32)(d0 = (u64)h0 + U8TOU32(inp + 0));
h1 = (u32)(d1 = (u64)h1 + (d0 >> 32) + U8TOU32(inp + 4));
h2 = (u32)(d2 = (u64)h2 + (d1 >> 32) + U8TOU32(inp + 8));
h3 = (u32)(d3 = (u64)h3 + (d2 >> 32) + U8TOU32(inp + 12));
h4 += (u32)(d3 >> 32) + padbit;
/* h *= r "%" p, where "%" stands for "partial remainder" */
d0 = ((u64)h0 * r0) +
((u64)h1 * s3) +
((u64)h2 * s2) +
((u64)h3 * s1);
d1 = ((u64)h0 * r1) +
((u64)h1 * r0) +
((u64)h2 * s3) +
((u64)h3 * s2) +
(h4 * s1);
d2 = ((u64)h0 * r2) +
((u64)h1 * r1) +
((u64)h2 * r0) +
((u64)h3 * s3) +
(h4 * s2);
d3 = ((u64)h0 * r3) +
((u64)h1 * r2) +
((u64)h2 * r1) +
((u64)h3 * r0) +
(h4 * s3);
h4 = (h4 * r0);
/* last reduction step: */
/* a) h4:h0 = h4<<128 + d3<<96 + d2<<64 + d1<<32 + d0 */
h0 = (u32)d0;
h1 = (u32)(d1 += d0 >> 32);
h2 = (u32)(d2 += d1 >> 32);
h3 = (u32)(d3 += d2 >> 32);
h4 += (u32)(d3 >> 32);
/* b) (h4:h0 += (h4:h0>>130) * 5) %= 2^130 */
c = (h4 >> 2) + (h4 & ~3U);
h4 &= 3;
h0 += c;
h1 += (c = CONSTANT_TIME_CARRY(h0,c));
h2 += (c = CONSTANT_TIME_CARRY(h1,c));
h3 += (c = CONSTANT_TIME_CARRY(h2,c));
h4 += CONSTANT_TIME_CARRY(h3,c);
/*
* Occasional overflows to 3rd bit of h4 are taken care of
* "naturally". If after this point we end up at the top of
* this loop, then the overflow bit will be accounted for
* in next iteration. If we end up in poly1305_emit, then
* comparison to modulus below will still count as "carry
* into 131st bit", so that properly reduced value will be
* picked in conditional move.
*/
inp += POLY1305_BLOCK_SIZE;
len -= POLY1305_BLOCK_SIZE;
}
st->h[0] = h0;
st->h[1] = h1;
st->h[2] = h2;
st->h[3] = h3;
st->h[4] = h4;
}
static void poly1305_emit(void *ctx, unsigned char mac[16],
const u32 nonce[4])
{
poly1305_internal *st = (poly1305_internal *) ctx;
u32 h0, h1, h2, h3, h4;
u32 g0, g1, g2, g3, g4;
u64 t;
u32 mask;
h0 = st->h[0];
h1 = st->h[1];
h2 = st->h[2];
h3 = st->h[3];
h4 = st->h[4];
/* compare to modulus by computing h + -p */
g0 = (u32)(t = (u64)h0 + 5);
g1 = (u32)(t = (u64)h1 + (t >> 32));
g2 = (u32)(t = (u64)h2 + (t >> 32));
g3 = (u32)(t = (u64)h3 + (t >> 32));
g4 = h4 + (u32)(t >> 32);
/* if there was carry into 131st bit, h3:h0 = g3:g0 */
mask = 0 - (g4 >> 2);
g0 &= mask;
g1 &= mask;
g2 &= mask;
g3 &= mask;
mask = ~mask;
h0 = (h0 & mask) | g0;
h1 = (h1 & mask) | g1;
h2 = (h2 & mask) | g2;
h3 = (h3 & mask) | g3;
/* mac = (h + nonce) % (2^128) */
h0 = (u32)(t = (u64)h0 + nonce[0]);
h1 = (u32)(t = (u64)h1 + (t >> 32) + nonce[1]);
h2 = (u32)(t = (u64)h2 + (t >> 32) + nonce[2]);
h3 = (u32)(t = (u64)h3 + (t >> 32) + nonce[3]);
U32TO8(mac + 0, h0);
U32TO8(mac + 4, h1);
U32TO8(mac + 8, h2);
U32TO8(mac + 12, h3);
}
# endif
#else
int poly1305_init(void *ctx, const unsigned char key[16], void *func);
void poly1305_blocks(void *ctx, const unsigned char *inp, size_t len,
unsigned int padbit);
void poly1305_emit(void *ctx, unsigned char mac[16],
const unsigned int nonce[4]);
#endif
void Poly1305_Init(POLY1305 *ctx, const unsigned char key[32])
{
ctx->nonce[0] = U8TOU32(&key[16]);
ctx->nonce[1] = U8TOU32(&key[20]);
ctx->nonce[2] = U8TOU32(&key[24]);
ctx->nonce[3] = U8TOU32(&key[28]);
#ifndef POLY1305_ASM
poly1305_init(ctx->opaque, key);
#else
/*
* Unlike reference poly1305_init assembly counterpart is expected
* to return a value: non-zero if it initializes ctx->func, and zero
* otherwise. Latter is to simplify assembly in cases when there no
* multiple code paths to switch between.
*/
if (!poly1305_init(ctx->opaque, key, &ctx->func)) {
ctx->func.blocks = poly1305_blocks;
ctx->func.emit = poly1305_emit;
}
#endif
ctx->num = 0;
}
#ifdef POLY1305_ASM
/*
* This "eclipses" poly1305_blocks and poly1305_emit, but it's
* conscious choice imposed by -Wshadow compiler warnings.
*/
# define poly1305_blocks (*poly1305_blocks_p)
# define poly1305_emit (*poly1305_emit_p)
#endif
void Poly1305_Update(POLY1305 *ctx, const unsigned char *inp, size_t len)
{
#ifdef POLY1305_ASM
/*
* As documented, poly1305_blocks is never called with input
* longer than single block and padbit argument set to 0. This
* property is fluently used in assembly modules to optimize
* padbit handling on loop boundary.
*/
poly1305_blocks_f poly1305_blocks_p = ctx->func.blocks;
#endif
size_t rem, num;
if ((num = ctx->num)) {
rem = POLY1305_BLOCK_SIZE - num;
if (len >= rem) {
memcpy(ctx->data + num, inp, rem);
poly1305_blocks(ctx->opaque, ctx->data, POLY1305_BLOCK_SIZE, 1);
inp += rem;
len -= rem;
} else {
/* Still not enough data to process a block. */
memcpy(ctx->data + num, inp, len);
ctx->num = num + len;
return;
}
}
rem = len % POLY1305_BLOCK_SIZE;
len -= rem;
if (len >= POLY1305_BLOCK_SIZE) {
poly1305_blocks(ctx->opaque, inp, len, 1);
inp += len;
}
if (rem)
memcpy(ctx->data, inp, rem);
ctx->num = rem;
}
void Poly1305_Final(POLY1305 *ctx, unsigned char mac[16])
{
#ifdef POLY1305_ASM
poly1305_blocks_f poly1305_blocks_p = ctx->func.blocks;
poly1305_emit_f poly1305_emit_p = ctx->func.emit;
#endif
size_t num;
if ((num = ctx->num)) {
ctx->data[num++] = 1; /* pad bit */
while (num < POLY1305_BLOCK_SIZE)
ctx->data[num++] = 0;
poly1305_blocks(ctx->opaque, ctx->data, POLY1305_BLOCK_SIZE, 0);
}
poly1305_emit(ctx->opaque, mac, ctx->nonce);
/* zero out the state */
OPENSSL_cleanse(ctx, sizeof(*ctx));
}