International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Practical Post-Quantum Signature Schemes from Isomorphism Problems of Trilinear Forms

Gang Tang , University of Technology Sydney
Dung Hoang Duong , University of Wollongong
Antoine Joux , CISPA Helmholtz Center for Information Security
Thomas Plantard , University of Wollongong
Youming Qiao , University of Technology Sydney
Willy Susilo , University of Wollongong
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Presentation: Slides
Conference: EUROCRYPT 2022
Abstract: In this paper, we propose a practical signature scheme based on the alternating trilinear form equivalence problem. Our scheme is inspired from the Goldreich-Micali-Wigderson's zero-knowledge protocol for graph isomorphism, and can be served as an alternative candidate for the NIST's post-quantum digital signatures. First, we present theoretical evidences to support its security, especially in the post-quantum cryptography context. The evidences are drawn from several research lines, including hidden subgroup problems, multivariate cryptography, cryptography based on group actions, the quantum random oracle model, and recent advances on isomorphism problems for algebraic structures in algorithms and complexity. Second, we demonstrate its potential for practical uses. Based on algorithm studies, we propose concrete parameter choices, and then implement a prototype. One concrete scheme achieves 128 bit security with public key size ~4100 bytes, signature size ~6800 bytes, and running times (key generation, sign, verify) ~0.8ms on a common laptop computer.
Video from EUROCRYPT 2022
  title={Practical Post-Quantum Signature Schemes from Isomorphism Problems of Trilinear Forms},
  author={Gang Tang and Dung Hoang Duong and Antoine Joux and Thomas Plantard and Youming Qiao and Willy Susilo},