Hybrid Meet-in-the-Middle Attacks for the Isogeny Path-Finding Problem

Yasuhiko Ikematsu, Ryoya Fukasaku, Momonari Kudo, Masaya Yasuda, Katsuyuki Takashima, Kazuhiro Yokoyama

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

Abstract

Isogeny-based cryptography has received attention as a candidate of post-quantum cryptography (PQC), and its security is based on the hardness of isogeny problems. The idea of meet-in-the-middle (MITM) is a bidirectional search for a collision, and it gives a powerful tool in cryptanalysis. In this paper, we propose hybrid approaches of MITM for solving the isogeny path-finding problem. Specifically, we first build part of trees of isogenies in a conventional way, and we then search a pair of isogenous curves of prime power degree by the algebraic approach using modular polynomials, proposed by Takahashi et al.¥! at MathCrypt 2019. Our hybrid approaches relax the requirements of sizes of search tables in MITM, and they also enable us to parallelize the part of algebraic search perfectly and easily. Here we show experimental results of our hybrid approaches to discuss a comparison with pure MITM approaches from a perspective of performance and sizes of search tables.

Original languageEnglish
Title of host publicationAPKC 2020 - Proceedings of the 7th ACM Workshop on ASIA Public-Key Cryptography, Co-located with AsiaCCS 2020
PublisherAssociation for Computing Machinery, Inc
Pages36-44
Number of pages9
ISBN (Electronic)9781450376075
DOIs
Publication statusPublished - Oct 5 2020
Event7th ACM Workshop on Asia Public-Key Cryptography, APKC 2020, held in conjunction with the 15th ACM ASIA Conference on Computer and Communications Security, ACM ASIACCS 2020 - Taipei, Taiwan, Province of China
Duration: Oct 6 2020 → …

Publication series

NameAPKC 2020 - Proceedings of the 7th ACM Workshop on ASIA Public-Key Cryptography, Co-located with AsiaCCS 2020

Conference

Conference7th ACM Workshop on Asia Public-Key Cryptography, APKC 2020, held in conjunction with the 15th ACM ASIA Conference on Computer and Communications Security, ACM ASIACCS 2020
CountryTaiwan, Province of China
CityTaipei
Period10/6/20 → …

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications
  • Information Systems
  • Software

Fingerprint Dive into the research topics of 'Hybrid Meet-in-the-Middle Attacks for the Isogeny Path-Finding Problem'. Together they form a unique fingerprint.

Cite this