[3/3] crypto: x86/ghash - add comment and fix broken link
Commit Message
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(-)
Comments
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.
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,
@@ -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>
@@ -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;
}