SCA-Resistant and Fast Elliptic Scalar Multiplication Based on wNAF (Asymmetric Cipher) (<Special Section>Cryptography and Information Security)

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概要

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• The side channel attack (SCA) is a serious attack on wearable devices that have scarce computational resources. Cryptographic algorithms on them should be efficient using small memory-we have to make efforts to optimize the trade-off between efficiency and memory. In this paper we present efficient SCA-resistant scalar multiplications based on window method. Moller proposed an SPA-resistant window method based on 2^ω-ary window method, which replaces tw-consecutive zeros to 1 plus to-consecutive 1 and it requires 2^ω points of table (or 2^<ω-1>+1 points if the signed 2^<ω-ary> is used). The most efficient window method with small memory is the width-ω NAF, which requires 2^<ω-2> points of table. In this paper we convert the width-ω NAF to an SPA-resistant addition chain. Indeed we generate a scalar sequence with the fixed pattern, e.g. |0 ・ ・ ・ 0x|0 ・ ・ ・ 0x| ・ ・ ・|0 ・ ・ ・ 0x|, where x is positive odd points < 2^ω. Thus the size of the table is 2^<ω-1>, which is optimal in the construction of the SPA-resistant chain based on width-ω NAF. The table sizes of the proposed scheme are 6% to 50% smaller than those of Moller's scheme for ω=2,3,4,5, which are relevant choices in the sense of efficiency for 160-bit ECC.

• 社団法人電子情報通信学会の論文
• 2004-01-01

著者

• OKEYA Katsuyuki

  Systems Development Laboratory, Hitachi Ltd.

• Takagi T

  Fachbereich Informatik Technische Universitat Darmstadt

• Okeya Katsuyuki

  Systems Development Laboratory Hitachi Ltd.

• TAKAGI Tsuyoshi

  Fachbereich Informatik, Technische Universitat Darmstadt

• Takagi Tsuyoshi

  Fachbereich Informatik Technische Universitat Darmstadt

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• Fast Elliptic Curve Multiplications with SIMD Operations (Asymmetric Cipher) (Cryptography and Information Security)
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• Defeating Simple Power Analysis on Koblitz Curves(Discrete Mathematics and Its Applications)
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• Cryptanalysis of Ha-Moon's Countermeasure of Randomized Signed Scalar Multiplication(Discrete Mathematics and Its Applications)
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