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+// 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");