Applied Coding Theory

Construction of quasi-cyclic alternant codes and their application in code-based cryptography

A. A. Kuninets^a, E. S. Malygina<sup>b

a</sup> Immanuel Kant Baltic Federal University, Kaliningrad, Russia
^b HSE, Moscow, Russia

Abstract: The paper presents an overview of quasi-cyclic alternant codes and their structural analysis regarding the classification of automorphisms. We also have detailed methods for recovering the structure of a given code. The attractiveness of the family of considered codes lies in their 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 subfield subcodes of quasi-cyclic algebraic-geometric codes associated with an arbitrary curve with a known group of automorphisms. However, 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: 10.17223/20710410/65/5