[PATCH 3/3] crypto: x86/ghash - add comment and fix broken link

[Eric Biggers <ebiggers@kernel.org>]

From: Eric Biggers <ebiggers@google.com>

Add a comment that explains what ghash_setkey() is doing, as it's hard
to understand otherwise.  Also fix a broken hyperlink.

Signed-off-by: Eric Biggers <ebiggers@google.com>
---
 arch/x86/crypto/ghash-clmulni-intel_asm.S  |  2 +-
 arch/x86/crypto/ghash-clmulni-intel_glue.c | 27 ++++++++++++++++++----
 2 files changed, 24 insertions(+), 5 deletions(-)

diff --git a/arch/x86/crypto/ghash-clmulni-intel_asm.S b/arch/x86/crypto/ghash-clmulni-intel_asm.S
index 9dfeb4d31b92..257ed9446f3e 100644
--- a/arch/x86/crypto/ghash-clmulni-intel_asm.S
+++ b/arch/x86/crypto/ghash-clmulni-intel_asm.S
@@ -4,7 +4,7 @@
  * instructions. This file contains accelerated part of ghash
  * implementation. More information about PCLMULQDQ can be found at:
  *
- * http://software.intel.com/en-us/articles/carry-less-multiplication-and-its-usage-for-computing-the-gcm-mode/
+ * https://www.intel.com/content/dam/develop/external/us/en/documents/clmul-wp-rev-2-02-2014-04-20.pdf
  *
  * Copyright (c) 2009 Intel Corp.
  *   Author: Huang Ying <ying.huang@intel.com>
diff --git a/arch/x86/crypto/ghash-clmulni-intel_glue.c b/arch/x86/crypto/ghash-clmulni-intel_glue.c
index 9453b094bb3b..700ecaee9a08 100644
--- a/arch/x86/crypto/ghash-clmulni-intel_glue.c
+++ b/arch/x86/crypto/ghash-clmulni-intel_glue.c
@@ -60,16 +60,35 @@ static int ghash_setkey(struct crypto_shash *tfm,
 	if (keylen != GHASH_BLOCK_SIZE)
 		return -EINVAL;
 
-	/* perform multiplication by 'x' in GF(2^128) */
+	/*
+	 * GHASH maps bits to polynomial coefficients backwards, which makes it
+	 * hard to implement.  But it can be shown that the GHASH multiplication
+	 *
+	 *	D * K (mod x^128 + x^7 + x^2 + x + 1)
+	 *
+	 * (where D is a data block and K is the key) is equivalent to:
+	 *
+	 *	bitreflect(D) * bitreflect(K) * x^(-127)
+	 *		(mod x^128 + x^127 + x^126 + x^121 + 1)
+	 *
+	 * So, the code below precomputes:
+	 *
+	 *	bitreflect(K) * x^(-127) (mod x^128 + x^127 + x^126 + x^121 + 1)
+	 *
+	 * ... but in Montgomery form (so that Montgomery multiplication can be
+	 * used), i.e. with an extra x^128 factor, which means actually:
+	 *
+	 *	bitreflect(K) * x (mod x^128 + x^127 + x^126 + x^121 + 1)
+	 *
+	 * The within-a-byte part of bitreflect() cancels out GHASH's built-in
+	 * reflection, and thus bitreflect() is actually a byteswap.
+	 */
 	a = get_unaligned_be64(key);
 	b = get_unaligned_be64(key + 8);
-
 	ctx->shash.a = cpu_to_le64((a << 1) | (b >> 63));
 	ctx->shash.b = cpu_to_le64((b << 1) | (a >> 63));
-
 	if (a >> 63)
 		ctx->shash.a ^= cpu_to_le64((u64)0xc2 << 56);
-
 	return 0;
 }
 
-- 
2.39.0