McELIECE CRYPTOSYSTEM BASED ON QUATERNARY HAMMING CODES
D. A. Isakov, A.V. Sokolov · INFORMATICS AND MATHEMATICAL METHODS IN SIMULATION · 2022
The operation of modern information protection systems is largely based on asymmetric cryptographic algorithms that allow encrypted information to be transmitted over an open communication channel without the need for prior key exchange.Modern asymmetric cryptographic algorithms are based on the use of such one-sided functions as factorization of large prime numbers and discrete logarithms, which require significant computational costs for their use, and are not resistant to promising quantum cryptanalysis attacks.Existing modifications of these cryptographic algorithms based on elliptic curves are also characterized by some significant drawbacks: many robust elliptic curves are currently patented, and algorithms on elliptic curves often require the use of powerful physical generators of truly random numbers.The solution to these problems is the use of the McEliece cryptographic system, which is based on the problem of decoding complete linear codes.Despite the prevailing performance of this system and its resistance to promising quantum cryptanalysis attacks, such a shortcoming as the large length of its public key has led to the fact that it is not often used in practice.In this paper, new families of Hamming (n,k)-codes in extensions of extended Galois fields are proposed and it is shown that on the basis of these codes a McEliece cryptosystem can be built, which is characterized by a much smaller size of the public key while providing a comparable number of generator matrices of the code so providing the comparable value of the protection levels number.The possibility of applying cascade Hamming codes on the extensions of extended Galois fields is shown, which makes it possible to obtain protection against the Sidelnikov attack.The proposed cryptosystem can be recommended for practical use in applications that require high speed (for example, mobile devices, IoT devices, and embedded systems), as well as significant cryptographic strength, including protection against promising quantum attacks.