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

Eric Biggers posted 3 patches 2 years, 9 months ago
[PATCH 3/3] crypto: x86/ghash - add comment and fix broken link
Posted by Eric Biggers 2 years, 9 months ago 
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
Re: [PATCH 3/3] crypto: x86/ghash - add comment and fix broken link
Posted by Peter Zijlstra 2 years, 9 months ago 
On Mon, Dec 19, 2022 at 09:40:42PM -0800, Eric Biggers wrote:
> 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

Since these things have a habbit if changing, we tend to prefer to host
a copy on kernel.org somewhere (used to be bugzilla, but perhaps there's
a better places these days).

>   *
>   * 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.
> +	 */

Whee, thanks, that was indeed entirely non-obvious.
Re: [PATCH 3/3] crypto: x86/ghash - add comment and fix broken link
Posted by Herbert Xu 2 years, 8 months ago 
On Tue, Dec 20, 2022 at 11:09:16AM +0100, Peter Zijlstra wrote:
> On Mon, Dec 19, 2022 at 09:40:42PM -0800, Eric Biggers wrote:
>
> > - * 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
> 
> Since these things have a habbit if changing, we tend to prefer to host
> a copy on kernel.org somewhere (used to be bugzilla, but perhaps there's
> a better places these days).

Alternatively just save a copy at web.archive.org when you submit
the patch and use that link.  In fact it seems that the original
link is still available via web.archive.org (sans pictures).

Cheers,
-- 
Email: Herbert Xu <herbert@gondor.apana.org.au>
Home Page: http://gondor.apana.org.au/~herbert/
PGP Key: http://gondor.apana.org.au/~herbert/pubkey.txt

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