Paper 2025/2171 Original: eprint.iacr.org/2025/2171 ↗

Efficient GHASH and POLYVAL Implementation Using Polynomial Multiplication: Optimized 64-bit Decomposition with Bit-Reversal Elimination

Abstract

We present an optimized implementation of the GHASH and POLYVAL authentication algorithms used in AES-GCM and AES-GCM-SIV that eliminates the computational overhead of bit-reversal operations. Our approach computes these universal hash functions directly in bit-reversed representation, matching the native format used by carry-less multiplication instructions available on modern processors. The algorithm exploits 64-bit polynomial primitives and parallel execution on superscalar architectures. We achieve performance of 0.34 cycles/byte on POWER9 (35% faster than OpenSSL) and 0.33 cycles/byte on Intel Comet Lake (11% faster than OpenSSL), representing a 32-fold improvement over table-based software implementations. Combined with hardware accelerated AES, the complete AES-GCM mode achieves 1.12 cycles/byte throughput. For platforms with hardware carry-less multiplication (x86 PCLMULQDQ, ARM PMULL, PowerPC vpmsumd), the R/F algorithm achieves ∼1.7× speedup over Karatsuba. For portable software implementations without hardware acceleration, we demonstrate that Karatsuba remains 1.4-1.6× faster due to reduced multiplication count.