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Updated 无进位乘法和GHASH (markdown)

Sun Yimin 2023-08-21 13:22:34 +08:00
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无进位乘法和GHASH.md

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* 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)