Abstract

tiple Data (SIMD) instructions (e.g. Intel-AVX, ARM-NEON) and a massive body of research on vector-parallel implementations of modular arithmetic, which are crucial components for modern public-key cryp-tography ranging from RSA, ElGamal, DSA and ECC, have been con-ducted. In this paper, we introduce a novel Double Operand Scanning (DOS) method to speed-up multi-precision squaring with non-redundant representations on SIMD architecture. The DOS technique partly dou-bles the operands and computes the squaring operation without Read-After-Write (RAW) dependencies between source and destination vari-ables. Furthermore, we presented Karatsuba Cascade Operand Scan-ning (KCOS) multiplication and Karatsuba Double Operand Scanning (KDOS) squaring by adopting additive and subtractive Karatsuba's meth-ods, respectively. The proposed multiplication and squaring methods are compatible with separated Montgomery algorithms and these are highly efficient for RSA crypto system. Finally, our proposed multiplica-tion/squaring, separated Montgomery multiplication/squaring and RSA encryption outperform the best-known results by 22/41%, 25/33 % and 30 % on the Cortex-A15 platform.