A preliminary study on methods to eliminate short fruitless cycles for pollard's rho method for ECDLP over BN Curves

Hiromasa Miura, Rikuya Matsumura, Ken Ikuta, Sho Joichi, Takuya Kusaka, Yasuyuki Nogami

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

Abstract

This paper discusses the conditions of fruitless cycles for Pollard's rho method with skew Frobenius mapping for elliptic curve discrete logarithm problem (ECDLP) over a Barreto-Naehrig (BN) curve. When a random walk pass achieves a fruitless cycle, the random walk pass must restart with a different starting point. There can be several methods to eliminate fruitless cycles of short lengths for BN curves based on the construction of a random walk table. Therefore, in this research, the authors give an analysis of the previous methods for a BN curve of order 349 with the mapping with experiments. The results show that several fruitless cycles of length two and three cannot be eliminated by the previous methods. The authors investigated the reason for degradation. As a result of the analysis, a new condition where a part of the fruitless cycles of any lengths occur is derived, and a new method to eliminate the fruitless cycles is proposed.

Original languageEnglish
Title of host publicationProceedings - 2019 7th International Symposium on Computing and Networking Workshops, CANDARW 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages353-359
Number of pages7
ISBN (Electronic)9781728152684
DOIs
Publication statusPublished - Nov 2019
Event7th International Symposium on Computing and Networking Workshops, CANDARW 2019 - Nagasaki, Japan
Duration: Nov 26 2019Nov 29 2019

Publication series

NameProceedings - 2019 7th International Symposium on Computing and Networking Workshops, CANDARW 2019

Conference

Conference7th International Symposium on Computing and Networking Workshops, CANDARW 2019
CountryJapan
CityNagasaki
Period11/26/1911/29/19

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Keywords

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

ASJC Scopus subject areas

  • Hardware and Architecture
  • Information Systems
  • Artificial Intelligence
  • Computer Networks and Communications

Cite this

Miura, H., Matsumura, R., Ikuta, K., Joichi, S., Kusaka, T., & Nogami, Y. (2019). A preliminary study on methods to eliminate short fruitless cycles for pollard's rho method for ECDLP over BN Curves. In Proceedings - 2019 7th International Symposium on Computing and Networking Workshops, CANDARW 2019 (pp. 353-359). [8951582] (Proceedings - 2019 7th International Symposium on Computing and Networking Workshops, CANDARW 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CANDARW.2019.00068