Post-quantum Cryptoschemes: New Finite Non-commutative Algebras for Defining Hidden Logarithm Problem

Nguyen, Hieu Minh; Moldovyan, Nikolay A.; Moldovyan, Alexander A.; Nguyen, Nam; Tran, Cong Manh; Phieu, Ngoc Han

doi:10.1007/978-3-030-06152-4_16

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

2018

DOI: 10.1007/978-3-030-06152-4_16

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Post-quantum Cryptoschemes: New Finite Non-commutative Algebras for Defining Hidden Logarithm Problem

Hieu Minh Nguyen

Nikolay A. Moldovyan

Alexander A. Moldovyan

et al.

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2020

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A New Method for Designing Post-Quantum Signature Schemes

Hieu¹,

Andreevich²,

Andreevich³

et al. 2020

jcm

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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.

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A New Method for Designing Post-Quantum Signature Schemes

Hieu¹,

Andreevich²,

Andreevich³

et al. 2020

jcm

View full text Add to dashboard Cite

show abstract

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Post-quantum Cryptoschemes: New Finite Non-commutative Algebras for Defining Hidden Logarithm Problem

Cited by 1 publication

References 10 publications

A New Method for Designing Post-Quantum Signature Schemes

A New Method for Designing Post-Quantum Signature Schemes

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