Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve

Yumi Sakemi, Goichiro Hanaoka, Tetsuya Izu, Masahiko Takenaka, Masaya Yasuda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

Abstract

A discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G, αG, α dG in an additive cyclic group generated by an element G of prime order r, and a positive integer d satisfying d|(r - 1). The infeasibility of this problem assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLPwAI (Cheon's algorithm). This paper reports our experimental results of Cheon's algorithm by implementing it with some speeding-up techniques. In fact, we have succeeded to solve DLPwAI on a pairing-friendly elliptic curve of 160-bit order in 1314 core days. Implications of our experiments on cryptographic schemes are also discussed.

Original languageEnglish
Title of host publicationPublic Key Cryptography, PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings
Pages595-608
Number of pages14
DOIs
Publication statusPublished - 2012
Event15th International Conference on Practice and Theory in Public Key Cryptography, PKC 2012 - Darmstadt, Germany
Duration: May 21 2012May 23 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7293 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th International Conference on Practice and Theory in Public Key Cryptography, PKC 2012
CountryGermany
CityDarmstadt
Period5/21/125/23/12

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve'. Together they form a unique fingerprint.

Cite this