Cryptology ePrint Archive: Report 2022/267

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

Gang Tang and Dung Hoang Duong and Antoine Joux and Thomas Plantard and Youming Qiao and Willy Susilo

Abstract: In this paper, we propose a practical signature scheme based on the alternating trilinear form equivalence problem. Our scheme is inspired by 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.

Category / Keywords: public-key cryptography / digital signatures, isomorphism problems, trilinear forms

Original Publication (with minor differences): IACR-EUROCRYPT-2022

Date: received 28 Feb 2022, last revised 12 Apr 2022

Contact author: hduong at uow edu au

Available format(s): PDF | BibTeX Citation

Version: 20220412:122029 (All versions of this report)

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