Improved Elliptic Curve Methods for Factoring and Their Performance (Special Section on Cryptography and Information Security)
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概要
- 論文の詳細を見る
Two methods of the second step of the elliptic curve method for factoring are known. One is the standard method that is similar to the second step of the p - 1 method, and the other is the Brent method that is based on the "birthday paradox." In this paper, we propose a revised standard method and a revised Brent method. On an average, the revised standard method is the most efficient, the standard method is the second efficient, the revised Brent method is the third and the Brent method is the fourth. If the largest prime factor on the order of an elliptic curve is congruent to 1 modulo 3, then the revised Brent method becomes more efficient than the standard method. By applying these methods to unsolved problems in the Cunningham project, we found 18 new prime factors. The largest prime factor among them was 43-digits.
- 一般社団法人電子情報通信学会の論文
- 1997-01-25
著者
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KOYAMA Kenji
NTT Communication Science Laboratories
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Kuwakado Hidenori
Ntt Communication Science Laboratories
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