A New Upper Bound for the Minimal Density of Joint Representations in Elliptic Curve Cryptosystems(<Special Section>Discrete Mathematics and Its Applications)
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概要
- 論文の詳細を見る
The most time consuming operation to verify a signature with the Elliptic Curve Digital Signature Algorithm is a multi-scalar multiplication with two scalars. Efficient methods for its computation are the Shamir method and the Interleave method, whereas the performance of those methods can be improved by using general base-2 representations of the scalars. In exchange for the speed-up, those representations require the precomputation of several points that must be stored. In the case of two precomputed points, the Interleave method and the Shamir method provide the same, optimal efficiency. In the case of more precomputed points, only the Interleave method can be sped-up in an optimal way and is currently more efficient than the Shamir method. This paper proposes a new general base-2 representation of the scalars that can be used to speed up the Shamir method. It requires the precomputation of ten points and is more efficient than any other representation that also requires ten precomputed points. Therefore, the proposed method is the first to improve the Shamir method such that it is faster than the Interleave method.
- 社団法人電子情報通信学会の論文
- 2007-05-01
著者
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OKEYA Katsuyuki
Systems Development Laboratory, Hitachi Ltd.
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TAKAGI Tsuyoshi
Future University-Hakodate
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Takagi Tsuyoshi
Future Univ.‐hakodate Hakodate‐shi Jpn
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Okeya Katsuyuki
Systems Development Laboratory Hitachi Ltd.
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DAHMEN Erik
Technische Universitat Darmstadt, Fachbereich Informatik
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Dahmen Erik
Technische Univ. Darmstadt Darmstadt Deu
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