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A New Method for Designing Post-Quantum Signature Schemes

Minh Nguyen Hieu 1, Moldovyan Alexander Andreevich 2, Moldovyan Nikolay Andreevich 2, and Canh Hoang Ngoc 3
1. Institute of Cryptographic Science and Technology, Hanoi, Vietnam
2. St.Petersburg Institute for Informatics and Automation of Russian Academy of Sciences, St.Petersburg, Russian
3. Thuongmai University, Hanoi, Vietnam

Abstract—The current standards of the digital signature algorithms are based on computational difficulty of the discrete logarithm and factorization problems. Expected appearance in near future of the quantum computer that is able to solve in polynomial time each of the said computational puts forward the actual task of the development of the post-quantum signature algorithms that resist the attacks using the quantum computers. Recently, the signature schemes based on the hidden discrete logarithm problem set in finite non-commutative associative algebras had been proposed. The paper is devoted to a further development of this approach and introduces a new practical post-quantum signature scheme possessing small size of public key and signature. The main contribution of the paper is the developed new method for defining the hidden discrete logarithm problem that allows applying the finite commutative groups as algebraic support of the post-quantum digital signature schemes. The method uses idea of applying multipliers that mask the periodicity connected with the value of discrete logarithm of periodic functions set on the base of the public parameters of the signature scheme. The finite 4-dimensional commutative associative algebra the multiplicative group of which possesses 4-dimensional cyclicity is used as algebraic support of the developed signature scheme.

Index Terms—Post-quantum cryptoschemes, computer security, digital signature, discrete logarithm problem, finite commutative algebra, hidden logarithm problem

Cite: Minh Nguyen Hieu, Moldovyan Alexander Andreevich, Moldovyan Nikolay Andreevich, and Canh Hoang Ngoc, "A New Method for Designing Post-Quantum Signature Schemes," Journal of Communications vol. 15, no. 10, pp. 747-754, October 2020. Doi: 10.12720/jcm.15.10.747-754

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