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

[Peter Zijlstra <peterz@infradead.org>]

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.