On the Issue of Constructing Matrices that Reduce Code Distance
摘要
This article explores the reduction of code distance as one of the factors in improving the efficiency of cryptographic code-based systems, particularly those based on the McEliece cryptosystem. Reducing code distance can directly impact the length of the public key, a crucial aspect in enhancing the performance and applicability of coding-based cryptosystems. The primary goal of the research is to develop an effective matrix construction algorithm capable of reducing code distance. The author proposes an iterative algorithm that generates masking matrices to successfully decrease the distance of a given code. The algorithm was applied to the BCH code, and the transformed code was integrated into the McEliece system. These transformed codes were tested against information set decoding attacks, demonstrating that they resistant to such attacks. Additionally, the weight of the generator matrix, a component of the public key, was reduced, enhancing the system’s overall efficiency. The practical significance of this work lies in its potential to reduce public key sizes in cryptographic systems, a factor critical for real-world applications. Beyond cryptography, the proposed approach could also be used in communication channels with memory. However, further research is needed to ensure the decodability of error vectors after applying the reverse transformation, which remains a key area for future investigation.