Effectiveness of a Method to Eliminate Fruitless Cycles for Pollard's Rho Method

Shota Kanzawa, Hiromasa Miura, Yuta Kodera, Yasuyuki Nogami, Takuya Kusaka

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

Abstract

In this research, the authors focus on an attack on a kind of pairing-friendly curves called the Barreto-Naehring curve. Accelerated attacks involve evaluating the security level concerning the elliptic curve discrete logarithm problem (ECDLP). The authors confirm the effectiveness of a method to eliminate a fruitless cycle in a random-walk path for parallel Pollard's rho method with skew Frobenius mapping for the curve. Though the rho method is known to solve the ECDLP efficiently, a random-walk path sometimes induces the unsolvable cycle, called a fruitless cycle, then the random-walk must restart with yet another starting point. In a previous work, the authors proposed a method to eliminate the fruitless cycle for a random-walk path. In this research, the authors implement a parallel rho method and confirm the effectiveness of the proposed method by several experiments. The results show that the proposed method effectively eliminate the fruitless cycles of length two and three, but increase the fruitless cycles of length four.

Original languageEnglish
Title of host publicationITC-CSCC 2022 - 37th International Technical Conference on Circuits/Systems, Computers and Communications
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages145-148
Number of pages4
ISBN (Electronic)9781665485593
DOIs
Publication statusPublished - 2022
Event37th International Technical Conference on Circuits/Systems, Computers and Communications, ITC-CSCC 2022 - Phuket, Thailand
Duration: Jul 5 2022Jul 8 2022

Publication series

NameITC-CSCC 2022 - 37th International Technical Conference on Circuits/Systems, Computers and Communications

Conference

Conference37th International Technical Conference on Circuits/Systems, Computers and Communications, ITC-CSCC 2022
Country/TerritoryThailand
CityPhuket
Period7/5/227/8/22

Keywords

  • Barreto-Naehrig curve
  • ECDLP
  • fruitless cycle
  • Pollard's rho method
  • skew Frobenius mapping

ASJC Scopus subject areas

  • Information Systems
  • Electrical and Electronic Engineering
  • Artificial Intelligence
  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture

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