Commutative Encryption Method Based on Hidden Logarithm Problem
Dmitriy Nikolaevich Moldovyan, Nikolay Andreevich Moldovyan, A.A. Moldovyan · Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software · 2020
A candidate for post-quantum commutative encryption algorithm is proposed, which is based on the hidden discrete logarithm problem defined in a new 6-dimensional finite noncommutative associative algebra.The properties of the algebra are investigated in detail and used in the design of the proposed commutative cipher.The formulas describing the set of p 2 different global right-sided units contained in the algebra and local left-sided units are derived.Homomorphisms of two different types are considered and used in the commutative cipher.The encrypted message is represented in the form of a locally invertible element T of the algebra and encryption procedure includes performing the exponentiation operation and homomorphism map followed by the left-sided multiplication by a randomly selected local right-sided unit.The introduced commutative cipher is secure to the knownplaintext attacks and has been used to develop the post-quantum no-key encryption protocol providing possibility to send securely a secret message via a public channel without using any pre-agreed key.The proposed commutative encryption algorithm is characterized in using the single-use keys that are selected at random directly during the encryption process.