Fast Elliptic Curve Multiplications with SIMD Operations

Tetsuya Izu, Tsuyoshi Takagi

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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 k-iterated ECDBL (k-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 k-bit zero run, we can replace k-time ECDBLs to the proposed faster k-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-w 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.

Original languageEnglish
Pages (from-to)85-93
Number of pages9
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE87-A
Issue number1
Publication statusPublished - Jan 1 2004

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Scalar multiplication
Elliptic Curves
Multiplication
Smart cards
Smart Card
Doubling
Addition Chains
Addition formula
Side Channel Attacks
Auxiliary Variables
Sliding Window
Fast Algorithm
Efficient Algorithms
Optimise
Binary
Zero

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

Fast Elliptic Curve Multiplications with SIMD Operations. / Izu, Tetsuya; Takagi, Tsuyoshi.

In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E87-A, No. 1, 01.01.2004, p. 85-93.

Research output: Contribution to journalArticle

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