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

Conference Paper


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) ≈ 0.8 ms on a common laptop computer.

Publication Date


  • 2022

Citation


  • Tang, G., Duong, D. H., Joux, A., Plantard, T., Qiao, Y., & Susilo, W. (2022). Practical Post-Quantum Signature Schemes from Isomorphism Problems of Trilinear Forms. In EUROCRYPT Vol. 13277 LNCS (pp. 582-612). doi:10.1007/978-3-031-07082-2_21

Scopus Eid


  • 2-s2.0-85132106269

Start Page


  • 582

End Page


  • 612

Volume


  • 13277 LNCS

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) ≈ 0.8 ms on a common laptop computer.

Publication Date


  • 2022

Citation


  • Tang, G., Duong, D. H., Joux, A., Plantard, T., Qiao, Y., & Susilo, W. (2022). Practical Post-Quantum Signature Schemes from Isomorphism Problems of Trilinear Forms. In EUROCRYPT Vol. 13277 LNCS (pp. 582-612). doi:10.1007/978-3-031-07082-2_21

Scopus Eid


  • 2-s2.0-85132106269

Start Page


  • 582

End Page


  • 612

Volume


  • 13277 LNCS