Abstract
The Single Instruction, Multiple Data (SIMD) architecture enables to compute in parallel on a single processor. The SIMD operations are implemented on some processors such as Pentium 3/4, Athlon, SPARC, and even on smart cards. This paper proposes efficient algorithms for assembling an elliptic curve addition (ECADD), doubling (ECDBL), and k-iterated ECDBL (k-ECDBL) with SIMD operations. Using the singed binary chain, we can compute a scalar multiplication about 10%faster than the previously fastest algorithm by Aoki et al. Combined with the sliding window method or the width-w NAF window method, we also achieve about 10% faster parallelized scalar multiplication algorithms with SIMD operations. For the implementation on smart cards, we propose two fast parallelized scalar multiplication algorithms with SIMD resistant against side channel attacks.
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Izu, T., Takagi, T. (2002). Fast Elliptic Curve Multiplications with SIMD Operations. In: Deng, R., Bao, F., Zhou, J., Qing, S. (eds) Information and Communications Security. ICICS 2002. Lecture Notes in Computer Science, vol 2513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36159-6_19
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DOI: https://doi.org/10.1007/3-540-36159-6_19
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