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

From: Eric Biggers
Date: Tue Dec 20 2022 - 00:42:18 EST


From: Eric Biggers <ebiggers@xxxxxxxxxx>

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@xxxxxxxxxx>
---
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@xxxxxxxxx>
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