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Updated 无进位乘法和GHASH (markdown)

Sun Yimin 2023-08-21 15:15:43 +08:00
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无进位乘法和GHASH.md

@ -19,7 +19,7 @@ $A_1 \cdot B_1 = [C_1 : C_0], \ A_0 \cdot B_0 = [D_1 : D_0]$
$(A_1 \oplus A_0) \cdot (B_1 \oplus B_0) = [E_1 : E_0]$ $(A_1 \oplus A_0) \cdot (B_1 \oplus B_0) = [E_1 : E_0]$
$[A_1 : A_0] \cdot [B_1 : B_0] = [C_1:C_0 \oplus C_1 \oplus D_1 \oplus E_1 : D_1 \oplus C_0 \oplus D_0 \oplus E_0 : D_0]$ $[A_1 : A_0] \cdot [B_1 : B_0] = [C_1:C_0 \oplus C_1 \oplus D_1 \oplus E_1 : D_1 \oplus C_0 \oplus D_0 \oplus E_0 : D_0]$
* A new interpretation to GHASH operations * A new interpretation to GHASH operations
* GHASH does not use $GF(2^{128})$ COMPUTATIONS "as expected" * GHASH does not use $GF(2^{128})$ computations "as expected"
* Not in the usual polynomial representation convention * Not in the usual polynomial representation convention
* The bits inside the 128-bit operands are reflected * The bits inside the 128-bit operands are reflected
* Actually - it is an operation on a permutation of elements of $GF(2^{128})$ * Actually - it is an operation on a permutation of elements of $GF(2^{128})$