| // SPDX-License-Identifier: GPL-2.0-or-later |
| /* |
| * POLYVAL library functions |
| * |
| * Copyright 2025 Google LLC |
| */ |
| |
| #include <crypto/polyval.h> |
| #include <linux/export.h> |
| #include <linux/module.h> |
| #include <linux/string.h> |
| #include <linux/unaligned.h> |
| |
| /* |
| * POLYVAL is an almost-XOR-universal hash function. Similar to GHASH, POLYVAL |
| * interprets the message as the coefficients of a polynomial in GF(2^128) and |
| * evaluates that polynomial at a secret point. POLYVAL has a simple |
| * mathematical relationship with GHASH, but it uses a better field convention |
| * which makes it easier and faster to implement. |
| * |
| * POLYVAL is not a cryptographic hash function, and it should be used only by |
| * algorithms that are specifically designed to use it. |
| * |
| * POLYVAL is specified by "AES-GCM-SIV: Nonce Misuse-Resistant Authenticated |
| * Encryption" (https://datatracker.ietf.org/doc/html/rfc8452) |
| * |
| * POLYVAL is also used by HCTR2. See "Length-preserving encryption with HCTR2" |
| * (https://eprint.iacr.org/2021/1441.pdf). |
| * |
| * This file provides a library API for POLYVAL. This API can delegate to |
| * either a generic implementation or an architecture-optimized implementation. |
| * |
| * For the generic implementation, we don't use the traditional table approach |
| * to GF(2^128) multiplication. That approach is not constant-time and requires |
| * a lot of memory. Instead, we use a different approach which emulates |
| * carryless multiplication using standard multiplications by spreading the data |
| * bits apart using "holes". This allows the carries to spill harmlessly. This |
| * approach is borrowed from BoringSSL, which in turn credits BearSSL's |
| * documentation (https://bearssl.org/constanttime.html#ghash-for-gcm) for the |
| * "holes" trick and a presentation by Shay Gueron |
| * (https://crypto.stanford.edu/RealWorldCrypto/slides/gueron.pdf) for the |
| * 256-bit => 128-bit reduction algorithm. |
| */ |
| |
| #ifdef CONFIG_ARCH_SUPPORTS_INT128 |
| |
| /* Do a 64 x 64 => 128 bit carryless multiplication. */ |
| static void clmul64(u64 a, u64 b, u64 *out_lo, u64 *out_hi) |
| { |
| /* |
| * With 64-bit multiplicands and one term every 4 bits, there would be |
| * up to 64 / 4 = 16 one bits per column when each multiplication is |
| * written out as a series of additions in the schoolbook manner. |
| * Unfortunately, that doesn't work since the value 16 is 1 too large to |
| * fit in 4 bits. Carries would sometimes overflow into the next term. |
| * |
| * Using one term every 5 bits would work. However, that would cost |
| * 5 x 5 = 25 multiplications instead of 4 x 4 = 16. |
| * |
| * Instead, mask off 4 bits from one multiplicand, giving a max of 15 |
| * one bits per column. Then handle those 4 bits separately. |
| */ |
| u64 a0 = a & 0x1111111111111110; |
| u64 a1 = a & 0x2222222222222220; |
| u64 a2 = a & 0x4444444444444440; |
| u64 a3 = a & 0x8888888888888880; |
| |
| u64 b0 = b & 0x1111111111111111; |
| u64 b1 = b & 0x2222222222222222; |
| u64 b2 = b & 0x4444444444444444; |
| u64 b3 = b & 0x8888888888888888; |
| |
| /* Multiply the high 60 bits of @a by @b. */ |
| u128 c0 = (a0 * (u128)b0) ^ (a1 * (u128)b3) ^ |
| (a2 * (u128)b2) ^ (a3 * (u128)b1); |
| u128 c1 = (a0 * (u128)b1) ^ (a1 * (u128)b0) ^ |
| (a2 * (u128)b3) ^ (a3 * (u128)b2); |
| u128 c2 = (a0 * (u128)b2) ^ (a1 * (u128)b1) ^ |
| (a2 * (u128)b0) ^ (a3 * (u128)b3); |
| u128 c3 = (a0 * (u128)b3) ^ (a1 * (u128)b2) ^ |
| (a2 * (u128)b1) ^ (a3 * (u128)b0); |
| |
| /* Multiply the low 4 bits of @a by @b. */ |
| u64 e0 = -(a & 1) & b; |
| u64 e1 = -((a >> 1) & 1) & b; |
| u64 e2 = -((a >> 2) & 1) & b; |
| u64 e3 = -((a >> 3) & 1) & b; |
| u64 extra_lo = e0 ^ (e1 << 1) ^ (e2 << 2) ^ (e3 << 3); |
| u64 extra_hi = (e1 >> 63) ^ (e2 >> 62) ^ (e3 >> 61); |
| |
| /* Add all the intermediate products together. */ |
| *out_lo = (((u64)c0) & 0x1111111111111111) ^ |
| (((u64)c1) & 0x2222222222222222) ^ |
| (((u64)c2) & 0x4444444444444444) ^ |
| (((u64)c3) & 0x8888888888888888) ^ extra_lo; |
| *out_hi = (((u64)(c0 >> 64)) & 0x1111111111111111) ^ |
| (((u64)(c1 >> 64)) & 0x2222222222222222) ^ |
| (((u64)(c2 >> 64)) & 0x4444444444444444) ^ |
| (((u64)(c3 >> 64)) & 0x8888888888888888) ^ extra_hi; |
| } |
| |
| #else /* CONFIG_ARCH_SUPPORTS_INT128 */ |
| |
| /* Do a 32 x 32 => 64 bit carryless multiplication. */ |
| static u64 clmul32(u32 a, u32 b) |
| { |
| /* |
| * With 32-bit multiplicands and one term every 4 bits, there are up to |
| * 32 / 4 = 8 one bits per column when each multiplication is written |
| * out as a series of additions in the schoolbook manner. The value 8 |
| * fits in 4 bits, so the carries don't overflow into the next term. |
| */ |
| u32 a0 = a & 0x11111111; |
| u32 a1 = a & 0x22222222; |
| u32 a2 = a & 0x44444444; |
| u32 a3 = a & 0x88888888; |
| |
| u32 b0 = b & 0x11111111; |
| u32 b1 = b & 0x22222222; |
| u32 b2 = b & 0x44444444; |
| u32 b3 = b & 0x88888888; |
| |
| u64 c0 = (a0 * (u64)b0) ^ (a1 * (u64)b3) ^ |
| (a2 * (u64)b2) ^ (a3 * (u64)b1); |
| u64 c1 = (a0 * (u64)b1) ^ (a1 * (u64)b0) ^ |
| (a2 * (u64)b3) ^ (a3 * (u64)b2); |
| u64 c2 = (a0 * (u64)b2) ^ (a1 * (u64)b1) ^ |
| (a2 * (u64)b0) ^ (a3 * (u64)b3); |
| u64 c3 = (a0 * (u64)b3) ^ (a1 * (u64)b2) ^ |
| (a2 * (u64)b1) ^ (a3 * (u64)b0); |
| |
| /* Add all the intermediate products together. */ |
| return (c0 & 0x1111111111111111) ^ |
| (c1 & 0x2222222222222222) ^ |
| (c2 & 0x4444444444444444) ^ |
| (c3 & 0x8888888888888888); |
| } |
| |
| /* Do a 64 x 64 => 128 bit carryless multiplication. */ |
| static void clmul64(u64 a, u64 b, u64 *out_lo, u64 *out_hi) |
| { |
| u32 a_lo = (u32)a; |
| u32 a_hi = a >> 32; |
| u32 b_lo = (u32)b; |
| u32 b_hi = b >> 32; |
| |
| /* Karatsuba multiplication */ |
| u64 lo = clmul32(a_lo, b_lo); |
| u64 hi = clmul32(a_hi, b_hi); |
| u64 mi = clmul32(a_lo ^ a_hi, b_lo ^ b_hi) ^ lo ^ hi; |
| |
| *out_lo = lo ^ (mi << 32); |
| *out_hi = hi ^ (mi >> 32); |
| } |
| #endif /* !CONFIG_ARCH_SUPPORTS_INT128 */ |
| |
| /* Compute @a = @a * @b * x^-128 in the POLYVAL field. */ |
| static void __maybe_unused |
| polyval_mul_generic(struct polyval_elem *a, const struct polyval_elem *b) |
| { |
| u64 c0, c1, c2, c3, mi0, mi1; |
| |
| /* |
| * Carryless-multiply @a by @b using Karatsuba multiplication. Store |
| * the 256-bit product in @c0 (low) through @c3 (high). |
| */ |
| clmul64(le64_to_cpu(a->lo), le64_to_cpu(b->lo), &c0, &c1); |
| clmul64(le64_to_cpu(a->hi), le64_to_cpu(b->hi), &c2, &c3); |
| clmul64(le64_to_cpu(a->lo ^ a->hi), le64_to_cpu(b->lo ^ b->hi), |
| &mi0, &mi1); |
| mi0 ^= c0 ^ c2; |
| mi1 ^= c1 ^ c3; |
| c1 ^= mi0; |
| c2 ^= mi1; |
| |
| /* |
| * Cancel out the low 128 bits of the product by adding multiples of |
| * G(x) = x^128 + x^127 + x^126 + x^121 + 1. Do this in two steps, each |
| * of which cancels out 64 bits. Note that we break G(x) into three |
| * parts: 1, x^64 * (x^63 + x^62 + x^57), and x^128 * 1. |
| */ |
| |
| /* |
| * First, add G(x) times c0 as follows: |
| * |
| * (c0, c1, c2) = (0, |
| * c1 + (c0 * (x^63 + x^62 + x^57) mod x^64), |
| * c2 + c0 + floor((c0 * (x^63 + x^62 + x^57)) / x^64)) |
| */ |
| c1 ^= (c0 << 63) ^ (c0 << 62) ^ (c0 << 57); |
| c2 ^= c0 ^ (c0 >> 1) ^ (c0 >> 2) ^ (c0 >> 7); |
| |
| /* |
| * Second, add G(x) times the new c1: |
| * |
| * (c1, c2, c3) = (0, |
| * c2 + (c1 * (x^63 + x^62 + x^57) mod x^64), |
| * c3 + c1 + floor((c1 * (x^63 + x^62 + x^57)) / x^64)) |
| */ |
| c2 ^= (c1 << 63) ^ (c1 << 62) ^ (c1 << 57); |
| c3 ^= c1 ^ (c1 >> 1) ^ (c1 >> 2) ^ (c1 >> 7); |
| |
| /* Return (c2, c3). This implicitly multiplies by x^-128. */ |
| a->lo = cpu_to_le64(c2); |
| a->hi = cpu_to_le64(c3); |
| } |
| |
| static void __maybe_unused |
| polyval_blocks_generic(struct polyval_elem *acc, const struct polyval_elem *key, |
| const u8 *data, size_t nblocks) |
| { |
| do { |
| acc->lo ^= get_unaligned((__le64 *)data); |
| acc->hi ^= get_unaligned((__le64 *)(data + 8)); |
| polyval_mul_generic(acc, key); |
| data += POLYVAL_BLOCK_SIZE; |
| } while (--nblocks); |
| } |
| |
| /* Include the arch-optimized implementation of POLYVAL, if one is available. */ |
| #ifdef CONFIG_CRYPTO_LIB_POLYVAL_ARCH |
| #include "polyval.h" /* $(SRCARCH)/polyval.h */ |
| void polyval_preparekey(struct polyval_key *key, |
| const u8 raw_key[POLYVAL_BLOCK_SIZE]) |
| { |
| polyval_preparekey_arch(key, raw_key); |
| } |
| EXPORT_SYMBOL_GPL(polyval_preparekey); |
| #endif /* Else, polyval_preparekey() is an inline function. */ |
| |
| /* |
| * polyval_mul_generic() and polyval_blocks_generic() take the key as a |
| * polyval_elem rather than a polyval_key, so that arch-optimized |
| * implementations with a different key format can use it as a fallback (if they |
| * have H^1 stored somewhere in their struct). Thus, the following dispatch |
| * code is needed to pass the appropriate key argument. |
| */ |
| |
| static void polyval_mul(struct polyval_ctx *ctx) |
| { |
| #ifdef CONFIG_CRYPTO_LIB_POLYVAL_ARCH |
| polyval_mul_arch(&ctx->acc, ctx->key); |
| #else |
| polyval_mul_generic(&ctx->acc, &ctx->key->h); |
| #endif |
| } |
| |
| static void polyval_blocks(struct polyval_ctx *ctx, |
| const u8 *data, size_t nblocks) |
| { |
| #ifdef CONFIG_CRYPTO_LIB_POLYVAL_ARCH |
| polyval_blocks_arch(&ctx->acc, ctx->key, data, nblocks); |
| #else |
| polyval_blocks_generic(&ctx->acc, &ctx->key->h, data, nblocks); |
| #endif |
| } |
| |
| void polyval_update(struct polyval_ctx *ctx, const u8 *data, size_t len) |
| { |
| if (unlikely(ctx->partial)) { |
| size_t n = min(len, POLYVAL_BLOCK_SIZE - ctx->partial); |
| |
| len -= n; |
| while (n--) |
| ctx->acc.bytes[ctx->partial++] ^= *data++; |
| if (ctx->partial < POLYVAL_BLOCK_SIZE) |
| return; |
| polyval_mul(ctx); |
| } |
| if (len >= POLYVAL_BLOCK_SIZE) { |
| size_t nblocks = len / POLYVAL_BLOCK_SIZE; |
| |
| polyval_blocks(ctx, data, nblocks); |
| data += len & ~(POLYVAL_BLOCK_SIZE - 1); |
| len &= POLYVAL_BLOCK_SIZE - 1; |
| } |
| for (size_t i = 0; i < len; i++) |
| ctx->acc.bytes[i] ^= data[i]; |
| ctx->partial = len; |
| } |
| EXPORT_SYMBOL_GPL(polyval_update); |
| |
| void polyval_final(struct polyval_ctx *ctx, u8 out[POLYVAL_BLOCK_SIZE]) |
| { |
| if (unlikely(ctx->partial)) |
| polyval_mul(ctx); |
| memcpy(out, &ctx->acc, POLYVAL_BLOCK_SIZE); |
| memzero_explicit(ctx, sizeof(*ctx)); |
| } |
| EXPORT_SYMBOL_GPL(polyval_final); |
| |
| #ifdef polyval_mod_init_arch |
| static int __init polyval_mod_init(void) |
| { |
| polyval_mod_init_arch(); |
| return 0; |
| } |
| subsys_initcall(polyval_mod_init); |
| |
| static void __exit polyval_mod_exit(void) |
| { |
| } |
| module_exit(polyval_mod_exit); |
| #endif |
| |
| MODULE_DESCRIPTION("POLYVAL almost-XOR-universal hash function"); |
| MODULE_LICENSE("GPL"); |