Fast elliptic curve multiplications with simd operations

Tetsuya Izu; Tsuyoshi Takagi

doi:10.1007/3-540-36159-6_19

Fast elliptic curve multiplications with simd operations

Tetsuya Izu, Tsuyoshi Takagi

Laboratory of Mathematical Design for Advanced Cryptography

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

21 Citations (Scopus)

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.

Original language	English
Title of host publication	Information and Communications Security - 4th International Conference, ICICS 2002, Proceedings
Editors	Robert Deng, Feng Bao, Jianying Zhou, Sihan Qing
Publisher	Springer Verlag
Pages	217-230
Number of pages	14
ISBN (Print)	3540001646
DOIs	https://doi.org/10.1007/3-540-36159-6_19
Publication status	Published - Jan 1 2002
Event	4th International Conference on Information and Communications Security, ICICS 2002 - Singapore, Singapore Duration: Dec 9 2002 → Dec 12 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2513
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	4th International Conference on Information and Communications Security, ICICS 2002
Country/Territory	Singapore
City	Singapore
Period	12/9/02 → 12/12/02

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-36159-6_19

Cite this

Izu, T., & Takagi, T. (2002). Fast elliptic curve multiplications with simd operations. In R. Deng, F. Bao, J. Zhou, & S. Qing (Eds.), Information and Communications Security - 4th International Conference, ICICS 2002, Proceedings (pp. 217-230). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2513). Springer Verlag. https://doi.org/10.1007/3-540-36159-6_19

Fast elliptic curve multiplications with simd operations. / Izu, Tetsuya; Takagi, Tsuyoshi.

Information and Communications Security - 4th International Conference, ICICS 2002, Proceedings. ed. / Robert Deng; Feng Bao; Jianying Zhou; Sihan Qing. Springer Verlag, 2002. p. 217-230 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2513).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Izu, T & Takagi, T 2002, Fast elliptic curve multiplications with simd operations. in R Deng, F Bao, J Zhou & S Qing (eds), Information and Communications Security - 4th International Conference, ICICS 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2513, Springer Verlag, pp. 217-230, 4th International Conference on Information and Communications Security, ICICS 2002, Singapore, Singapore, 12/9/02. https://doi.org/10.1007/3-540-36159-6_19

Izu T, Takagi T. Fast elliptic curve multiplications with simd operations. In Deng R, Bao F, Zhou J, Qing S, editors, Information and Communications Security - 4th International Conference, ICICS 2002, Proceedings. Springer Verlag. 2002. p. 217-230. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-36159-6_19

Izu, Tetsuya ; Takagi, Tsuyoshi. / Fast elliptic curve multiplications with simd operations. Information and Communications Security - 4th International Conference, ICICS 2002, Proceedings. editor / Robert Deng ; Feng Bao ; Jianying Zhou ; Sihan Qing. Springer Verlag, 2002. pp. 217-230 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Fast elliptic curve multiplications with simd operations

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