Collision of random walks and a refined analysis of attacks on the discrete logarithm problem

Shuji Kijima, Ravi Montenegro

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

2 被引用数 (Scopus)

抄録

Some of the most efficient algorithms for finding the discrete logarithm involve pseudo-random implementations of Markov chains, with one or more “walks” proceeding until a collision occurs, i.e. some state is visited a second time. In this paper we develop a method for determining the expected time until the first collision. We use our technique to examine three methods for solving discrete-logarithm problems: Pollard’s Kangaroo, Pollard’s Rho, and a few versions of Gaudry-Schost. For the Kangaroo method we prove new and fairly precise matching upper and lower bounds. For the Rho method we prove the first rigorous non-trivial lower bound, and under a mild assumption show matching upper and lower bounds. Our Gaudry-Schost results are heuristic, but improve on the prior limited understanding of this method. We also give results for parallel versions of these algorithms.

本文言語英語
ホスト出版物のタイトルPublic-Key Cryptography - PKC 2015 - 18th IACR International Conference on Practice and Theory in Public-Key Cryptography, Proceedings
編集者Jonathan Katz
出版社Springer Verlag
ページ127-149
ページ数23
ISBN(電子版)9783662464465
DOI
出版ステータス出版済み - 2015
イベント18th IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2015 - Gaithersburg, 米国
継続期間: 3 30 20154 1 2015

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
9020
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他18th IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2015
国/地域米国
CityGaithersburg
Period3/30/154/1/15

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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