Parallel modular multiplication using 512-bit advanced vector instructions

Abstract Applications such as public-key cryptography are critically reliant on the speed of modular multiplication for their performance. This paper introduces a new block-based variant Montgomery multiplication, Block Product Scanning (BPS) method, which is particularly efficient using 512-bit advanced vector instructions (AVX-512) modern Intel processor families. Our parallel-multiplication approach also allows squaring and sub-quadratic Karatsuba enhancements. We demonstrate $$1.9\,\times $$ 1.9 × improvement in decryption throughput comparison with OpenSSL $$1.5\,\times 1.5 exponentiation compared to GMP-6.1.2 an Xeon CPU. In addition, we show $$1.4\,\times 1.4 state-of-the-art implementations many-core Knights Landing Phi hardware. Finally, how interleaving Chinese remainder theorem-based RSA calculations within our parallel BPS technique halves latency while providing protection against fault-injection attacks.