Post-quantum commutative deniable encryption algorithm

There is proposed a new post-quantum commutative encryption algorithm based on the hidden discrete logarithm problem. The introduced cipher is suitable for implementing post-quantum pseudo-probabilistic deniable encryption protocol. The proposed commutative cipher belongs to the class of the algebraic ciphers. Its algebraic support represents a finite noncommutative associative algebra of special type. The used algebra is characterized in existence of a large set of the global right-sided units that are used to define the homomorphism map of the algebra and then to define the hidden discrete logarithm problem using the mutual commutativity of the homomorphism-map operation and the exponentiation operation. The proposed commutative cipher is the first implementation of the post-quantum commutative ciphers based on the hidden discrete logarithm problem defined in a finite algebra that contains no two-sided global unit. © Springer Nature Singapore Pte Ltd. 2020.