Paper 2021/906

Expanded Gabidulin Codes and Their Application to Cryptography

Wenshuo Guo and Fang-Wei Fu

Abstract

This paper presents a new family of linear codes, namely the expanded Gabidulin codes. Exploiting the existing fast decoder of Gabidulin codes, we propose an efficient algorithm to decode these new codes when the noise vector satisfies a certain condition. Further more, these new codes enjoy an excellent error-correcting capability because of the optimality of their parent Gabidulin codes. Based on different masking techniques, we give two encryption schemes by using expanded Gabidulin codes in the McEliece setting. According to our analysis, both of these two cryptosystems can resist the existing structural attacks. Compared to some other code-based cryptosystems, our proposals have obvious advantage in public-key representation without using the cyclic or quasi-cyclic structure.