Fast Elliptic Curve Multiplications with SIMD Operations (Asymmetric Cipher) (<Special Section>Cryptography and Information Security)

概要

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The Single Instruction, Multiple Data (SIMD) architecture enables computation in parallel on a single processor. The SIMD operations are implemented on some processors such as Pentium 3/4, Athlon, SPARC, or even on smart cards. This paper proposes efficient algorithms for assembling an elliptic curve addition (ECADD), doubling (ECDBL), and κ-iterated ECDBL (κ-ECDBL) with SIMD operations. We optimize the number of auxiliary variables and the order of basic field operations used for these addition formulas. If an addition chain has κ-bit zero run, we can replace κ-time ECDBLs to the proposed faster κ-ECDBL and the total efficiency of the scalar multiplication can be improved. Using the singed binary chain, we can compute a scalar multiplication about 10% faster than the previously fastest algorithm proposed by Aoki et al. Combined with the sliding window method or the width-ω NAF window method, we also achieve about 10% faster parallelized scalar multiplication algorithms with SIMD operations. For the implementation on smart cards, we establish two fast parallelized scalar multiplication algorithms with SIMD resistant against side channel attacks.
社団法人電子情報通信学会の論文
2004-01-01