Solving DLP with auxiliary input over an elliptic curve used in TinyTate library

Yumi Sakemi, Tetsuya Izu, Masahiko Takenaka, Masaya Yasuda

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

2 Citations (Scopus)

Abstract

The 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 G of prime order r and a positive integer d dividing r-1. The infeasibility of DLPwAI assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLPwAI. This paper shows our experimental results of Cheon's algorithm by implementing it with some speeding-up techniques. In fact, we succeeded to solve DLPwAI in a group with 128-bit order in 45 hours with a single PC on an elliptic curve defined over a prime finite field with 256-bit elements which is used in the TinyTate library.

Original languageEnglish
Title of host publicationInformation Security Theory and Practice
Subtitle of host publicationSecurity and Privacy of Mobile Devices in Wireless Communication - 5th IFIP WG 11.2 International Workshop, WISTP 2011, Proceedings
Pages116-127
Number of pages12
DOIs
Publication statusPublished - Jun 20 2011
Externally publishedYes
Event5th Workshop in Information Security Theory and Practice, WISTP 2011 - Heraklion, Crete, Greece
Duration: Jun 1 2011Jun 3 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6633 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th Workshop in Information Security Theory and Practice, WISTP 2011
CountryGreece
CityHeraklion, Crete
Period6/1/116/3/11

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Sakemi, Y., Izu, T., Takenaka, M., & Yasuda, M. (2011). Solving DLP with auxiliary input over an elliptic curve used in TinyTate library. In Information Security Theory and Practice: Security and Privacy of Mobile Devices in Wireless Communication - 5th IFIP WG 11.2 International Workshop, WISTP 2011, Proceedings (pp. 116-127). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6633 LNCS). https://doi.org/10.1007/978-3-642-21040-2_8