Speeding Up Elliptic Scalar Multiplication Using Multidoubling(Special Section on Discrete Mathematics and Its Applications)

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概要

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• We discuss multidoubling methods for efficient elliptic scalar multiplication. The methods allows computation of 2^k p directly from P without computing the intermediate points, where P denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic curves with Montgomery form and Weierstrass form defined over finite fields with characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves and analyze computational complexity. As a result of our implementation with respect to the Montgomery and Weierstrass forms in terms of affine coordinates, we achieved running time reduced by 28% and 31%, respectively, in the scalar multiplication of an elliptic curve of size 160-bit over finite fields with characteristic greater than 3.

• 社団法人電子情報通信学会の論文
• 2002-05-01

著者

• SAKURAI Kouichi

  The author is with the Faculty of Kyusyu University

• Sakai Yasuyuki

  The Author Is With Information Technology R&d Center Mitsubishi Electric Corporation

• Sakurai Kouichi

  The Author Is With The Faculty Of Engineering Kyushu University

関連論文

• On the Practical Performance of Hyperelliptic Curve Cryptosystems in Software Implementation(Special Section on Discrete Mathematics and Its Applications)
• Efficient Scalar Multiplications on Elliptic Curves with Direct Computations of Several Doublings : Special Section on Cryptography and Information Security
• Speeding Up Elliptic Scalar Multiplication Using Multidoubling(Special Section on Discrete Mathematics and Its Applications)
• A Theory of Demonstrating Program Result-Correctness with Cryptographic Applications (Special lssue on Selected Papers from LA Synposium)

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