ANAMORPHIC CRYPTOSYSTEM BASED ON McELIECE-TYPE CONSTRUCTION OVER NON-BINARY FIELDS

Abstract

Сonsiders an approach to the construction of an asymmetric cryptographic system that combines methods of code-based cryptography with an anamorphic encryption mechanism, in which the same ciphertext may admit different informational interpretations depending on the secret parameters available to the receiver. The proposed approach is based on using the error vector of code-based encryption not only as a masking mechanism for the transmitted message but also as an additional carrier of hidden information, without violating the correctness of decryption of the main channel. An asymmetric anamorphic cryptosystem based on a modified McEliece-like construction using GRS codes over finite Galois fields GF(p) is implemented. To align the parameters of the messages with the code construction of the system, a transition to the residue number system is applied, which reduces the bit-width of arithmetic operations and computational costs while preserving the cryptographic properties of the scheme, and also enables adaptation of the capacities of the main and hidden channels without modifying the cryptographic core. A theoretical analysis and experimental evaluation of the efficiency of the proposed solution are carried out. The scalability of code parameters, timing characteristics of the main cryptographic operations, the impact of the hidden channel on ciphertext and key sizes, and robustness against additional errors are analyzed. It is shown that the implementation of the hidden anamorphic channel does not alter the structure of the public key, does not affect the statistical properties of the ciphertext, and does not reduce the error-correcting capability of the code. The obtained results indicate that the cryptographic security of the proposed system is based on the hardness of decoding random non-binary linear codes with errors. The proposed approach is promising for applications in secure and covert information transmission systems.