This paper proposes an improvement of the McEliece asymmetric cryptosystem based on code-based cryptography by replacing the permutation matrix with a modulo operation and using a finite field $GF(q)$.
This approach increases the complexity of the decryption process for potential attackers, providing a high level of cryptographic security without changing the length of the key. The article provides a diagram of the improved operation of the cryptosystem and describes examples of application. An analysis of the number of possible combinations of matrices has been carried out for different implementation options of code (7,4) based on different numerical systems. It has been shown that achieving cryptographic security comparable to the original McEliece cryptosystem requires the use of $q ≥ 5$.
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