无进位乘法和GHASH

概述

参考Reference 1，Page 35 - 39

• The PCLMULQDQ + AES-NI combination for AES-GCM
  • AES-NI facilitate high performance AES encryption and decryption
  • 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:
    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)

参考

• Cryptographic Hardware and Software and useful architectures
• The Galois/Counter Mode of Operation (GCM)
• Recommendation for Block Cipher Modes of Operation: Galois/Counter Mode (GCM) and GMAC
• Intel® Carry-Less Multiplication Instruction and its Usage for Computing the GCM Mode
• Optimized Galois-Counter Mode implementation on Intel® Architecture Processors
• Enabling High Performance Galois-Counter Mode on Intel® Architecture Processors