From d9d7d2722c4210a769f4df0b3acda969efada598 Mon Sep 17 00:00:00 2001 From: Sun Yimin Date: Mon, 21 Aug 2023 13:58:56 +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 462aef4..4064b19 100644 --- a/无进位乘法和GHASH.md +++ b/无进位乘法和GHASH.md @@ -10,11 +10,11 @@ 2. Reduction: ${256 \rightarrow 128} \ modulo \ {x^{128} + x^7 + x^2 + x + 1}$ (done efficiently via software) * 128-bit Carry-less Multiplication using PCLMULQDQ (Gueron Kounavis, 2009) Multiply $128 \times 128 \rightarrow 256 \ [A_1 : A_0]\cdot[B_1 : B_0]$ - * Schoolbook (4 PCLMULQDQ invocations) + * **Schoolbook** (4 PCLMULQDQ invocations) $A_0 \cdot B_0 = [C_1 : C_0], \ A_1 \cdot B_1 = [D_1 : D_0]$ $A_0 \cdot B_1 = [E_1 : E_0], \ A_1 \cdot B_0 = [F_1 : F_0]$ $[A_1 : A_0] \cdot [B_1 : B_0] = [D_1:D_0 \oplus E_1 \oplus F_1:C_1 \oplus E_0 \oplus F_0 : C_0]$ - * Carry-less Karatsuba (3 PCLMULQDQ invocations) + * **Carry-less Karatsuba** (3 PCLMULQDQ invocations) $A_1 \cdot B_1 = [C_1 : C_0], \ A_0 \cdot B_0 = [D_1 : D_0]$ $(A_1 \oplus A_0) \cdot (B_1 \oplus B_0) = [E_1 : E_0]$ $[A_1 : A_0] \cdot [B_1 : B_0] = [C_1:C_0 \oplus C_1 \oplus D_1 \oplus E_1 : D_1 \oplus C_0 \oplus D_0 \oplus E_0 : D_0]$