**Authors:** A.A. Moldovyan, D.N. Moldovyan, N.A. Moldovyan

**Keywords:** commutative encryption, post-quantum cryptoscheme, no-key protocol, finite non-commutative algebra, associative algebra, homomorphism

### Abstract

To provide possibility to design the commutative encryption algorithms on the basis of new versions of the hidden discrete logarithm problem, the term "commutativity" is interpreted in the extended sense. Namely, the encryption algorithm is called commutative, if the double encryption on two different keys produces the ciphertext that can be correctly decrypted using the keys in arbitrary order. The introduced commutative encryption method is characterized in using the single-use random subkeys. This feature defines probabilistic nature of the encryption process. A candidate for post-quantum commutative encryption algorithm is proposed, using the computations in the 6-dimensional finite non-commutative associative algebra with a large set of the right-sided global units. The proposed algorithm is used as the base of the post-quantum no-key protocol.

St. Petersburg Institute for Informatics and Automation

of Russian Academy of Sciences,

14 Liniya, 39, St. Petersburg 199178, Russia

E-mail: , ,

http://www.spiiras.nw.ru
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