Security and Complexity of a New Variant of the McEliece Cryptosystem Using Non-linear Convolutional Codes

Abstract

The McEliece public-key cryptography (PKC) has fewer encryption/decryption operations compared to other PKC schemes such as RSA, ECC, and ElGamal. The use of Goppa codes in its implementation ensures the hardness of the decoding problem. Conversely, the original McEliece PKC has a low encryption rate and large key size. In this paper, a new variant of the McEliece cryptosystem is presented based on non-linear convolutional codes. Cascaded convolutional codes are used to be part of the public key with each stage of the cascade separated by a product cipher to increase the security level. Convolutional codes are used as an alternative to Goppa codes since the Viterbi decoding algorithm is suitable for high data-rate applications by providing maximum-likelihood solutions. The convolutional code used in the implementation increases both security and throughput due to its high error-correcting capacity. It is shown that the new variant has small key sizes with enhanced security-complexity trade-off. Cryptanalysis of the new version of the McEliece cryptosystem is performed using existing attacks of the classical cryptosystem to demonstrate the difficulties in breaking the new cryptosystem. Also, it is shown that security levels comparable to the original McEliece cryptosystem could be obtained by using smaller public key sizes of the new version if multiple stages of the generator matrix are employed. This aspect makes the new version of the McEliece cryptosystem attractive in mobile wireless networks since it could be ported onto a single Field Programmable Gate Array (FPGA).