Analysis of a method to eliminate fruitless cycles for Pollard’s rho method with skew Frobenius mapping over a Barreto-Naehrig curve

Hiromasa Miura, Rikuya Matsumura, Takuya Kusaka, Yasuyuki Nogami

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

Abstract

Pollard’s rho method is one of the most efficient methods for solving elliptic curve discrete logarithm problem (ECDLP) in elliptic curve cryptography. Pollard’s rho method with skew Frobenius mapping can solve ECDLP over a Barreto-Naehrig (BN) curve efficiently. Pollard’s rho method may result in an unsolvable cycle called a fruitless cycle. When a random walk pass results in a fruitless cycle, the random walk pass must restart with a different starting point. However, an effective method for eliminating the fruitless cycle has been not proposed yet. This paper proposes a method for eliminating the fruitless cycle in Pollard’s rho method with skew Frobenius mapping. In addition, the authors apply the proposed method to a BN curve with 17-bit parameters and confirm the effectiveness.

Original languageEnglish
Title of host publicationProceedings - 2020 8th International Symposium on Computing and Networking, CANDAR 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages160-166
Number of pages7
ISBN (Electronic)9781728182216
DOIs
Publication statusPublished - Nov 2020
Event8th International Symposium on Computing and Networking, CANDAR 2020 - Virtual, Naha, Japan
Duration: Nov 24 2020Nov 27 2020

Publication series

NameProceedings - 2020 8th International Symposium on Computing and Networking, CANDAR 2020

Conference

Conference8th International Symposium on Computing and Networking, CANDAR 2020
Country/TerritoryJapan
CityVirtual, Naha
Period11/24/2011/27/20

Keywords

  • Barreto-Naehrig curve
  • ECDLP
  • Fruitless cycle
  • Pollard’s rho method
  • Skew Frobenius mapping

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Computer Science Applications
  • Software

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