Applied Theory of Coding, Automata and Graphs

Quasi-cyclic alternant codes and analysis of their security in cryptographic applications

A. A. Kuninets

Immanuel Kant Baltic Federal University, Kaliningrad

Abstract: The paper presents an overview of quasi-cyclic alternant codes and their structural analysis regarding the classification of automorphisms. Also, we describe in detail methods for restoring the structure of a given code. The attractiveness of the family of considered codes lies in its cryptographic applications, and, as in theory, in reducing the key length of post-quantum code-based schemes. In addition, this method of constructing codes is universal and can be used to obtain alternant codes of quasi-cyclic algebraic-geometric codes associated with an arbitrary curve with a known group of automorphisms. However, as shown in the work, as a result of constructing quasi-cyclic alternant codes, it becomes possible to reduce the key security of the source code to a code with smaller parameters, which may not be resistant to a structural attack.

Keywords: quasi-cyclic codes, alternant codes, invariant codes, algebraic-geometric code, function fields, automorphism group of a code.

UDC: 519.17

DOI: 10.17223/2226308X/17/38