**Authors:** D. N. Moldovyan

**Keywords:** finite non-commutative algebra, associative algebra, computationally difficult problem, homomorphism, key agreement scheme, zero-knowledge protocol, post-quantum cryptoscheme

### Abstract

A new form of the hidden discrete logarithm problem, proposed as primitive of the post-quantum public-key cryptoschemes, is defined over the 6-dimensional finite non-commutative associative algebra with a large set of the left-sided global units. The considered computationally difficult problem uses the mutual commutativity of the exponentiation operation and homomorphism mapping defined relatively a fixed unit element of the algebra. The related properties of the introduced algebra are described. Novel public key-agreement and zero-knowledge protocols based on the hidden logarithm problem are introduced as post-quantum cryptoschemes.

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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