Solving 114-bit ECDLP for barreto-naehrig curve

Takuya Kusaka, Sho Joichi, Ken Ikuta, Md Al Amin Khandaker, Yasuyuki Nogami, Satoshi Uehara, Nariyoshi Yamai, Sylvain Duquesne

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

4 Citations (Scopus)

Abstract

The security of cryptographic protocols which are based on elliptic curve cryptography relies on the intractability of elliptic curve discrete logarithm problem (ECDLP). In this paper, the authors describe techniques applied to solve 114-bit ECDLP in Barreto-Naehrig (BN) curve defined over the odd characteristic field. Unlike generic elliptic curves, BN curve holds an especial interest since it is well studied in pairing-based cryptography. Till the date of our knowledge, the previous record for solving ECDLP in a prime field was 112-bit by Bos et al. in Certicom curve ‘secp112r1’. This work sets a new record by solving 114-bit prime field ECDLP of BN curve using Pollard’s rho method. The authors utilized sextic twist property of the BN curve to efficiently carry out the random walk of Pollard’s rho method. The parallel implementation of the rho method by adopting a client-server model, using 2000 CPU cores took about 6 months to solve the ECDLP.

Original languageEnglish
Title of host publicationInformation Security and Cryptology - ICISC 2017 - 20th International Conference, Revised Selected Papers
PublisherSpringer Verlag
Pages231-244
Number of pages14
ISBN (Print)9783319785554
DOIs
Publication statusPublished - Jan 1 2018
Event20th International Conference on International Conference on Information Security and Cryptology, ICISC 2017 - Seoul, Korea, Republic of
Duration: Nov 29 2017Dec 1 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10779 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other20th International Conference on International Conference on Information Security and Cryptology, ICISC 2017
CountryKorea, Republic of
CitySeoul
Period11/29/1712/1/17

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Keywords

  • Barreto-Naehrig curve
  • ECDLP
  • Pollard’s rho method

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kusaka, T., Joichi, S., Ikuta, K., Khandaker, M. A. A., Nogami, Y., Uehara, S., Yamai, N., & Duquesne, S. (2018). Solving 114-bit ECDLP for barreto-naehrig curve. In Information Security and Cryptology - ICISC 2017 - 20th International Conference, Revised Selected Papers (pp. 231-244). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10779 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-78556-1_13