From 152f75e7c04ad4ceb15df8283f50371566dc1bbd Mon Sep 17 00:00:00 2001 From: Sun Yimin Date: Mon, 21 Aug 2023 13:22:34 +0800 Subject: [PATCH] =?UTF-8?q?Updated=20=E6=97=A0=E8=BF=9B=E4=BD=8D=E4=B9=98?= =?UTF-8?q?=E6=B3=95=E5=92=8CGHASH=20(markdown)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 无进位乘法和GHASH.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/无进位乘法和GHASH.md b/无进位乘法和GHASH.md index b33046b..cb0b36f 100644 --- a/无进位乘法和GHASH.md +++ b/无进位乘法和GHASH.md @@ -5,9 +5,9 @@ * PCLMULQDQ ```64 x 64 -> 128 (carry-less)``` * Binary polynomial multiplication; speed up computations in binary fields * Using it for AES-GCM: - * To use it for GHASH computations: GF(2^128) multiplication: + * To use it for GHASH computations: GF($2^{128}$) multiplication: 1. Compute ```128 x 128 -> 256``` via carry-less multiplication (of 64-bit operands) - 2. Reduction: ```256 -> 128 modulo x^128 + x^7 + x^2 + x + 1``` (done efficiently via software) + 2. Reduction: 256 -> 128 modulo $x^{128} + x^7 + x^2 + x + 1$ (done efficiently via software) # 参考 * [Cryptographic Hardware and Software and useful architectures](https://www.esat.kuleuven.be/cosic/events/ecrypt-net-school-2018/wp-content/uploads/sites/23/2018/10/kos-school-gueron-2.pdf)