Algebraic Supports and New Forms of the Hidden Discrete Logarithm Problem for Post-quantum Public-key Cryptoschemes

Abstract

This paper introduces two new forms of the hidden discrete logarithm problem defined over a finite non-commutative associative algebras containing a large set of global single-sided units. The proposed forms are promising for development on their base practical post-quantum public key-agreement schemes and are characterized in performing two different masking operations over the output value of the base exponentiation operation that is executed in framework of the public key computation. The masking operations represent homomorphisms and each of them is mutually commutative with the exponentiation operation. Parameters of the masking operations are used as private key elements. A 6-dimensional algebra containing a set of p3 global left-sided units is used as algebraic support of one of the hidden logarithm problem form and a 4-dimensional algebra with p2 global right-sided units is used to implement the other form of the said problem. The result of this paper is the proposed two methods for strengthened masking of the exponentiation operation and two new post-quantum public key-agreement cryptoschemes. Mathematics subject classification: 94A60, 16Z05, 14G50, 11T71, 16S50.

Quantum public key encryption scheme with four states key

“…Recently, Li [20] proposed a QPKE scheme based on conjugate coding [21]. Also there are many other reaserch about QPKE [22][23][24][25][26][27][28][29][30][31][32].…”