Abstract
In this paper the basic principles of construction and operation of McEliece and Niederreiter cryptosystems based on the use of error-correcting codes were considered. A new hybrid cryptosystem that combines the rules of encryption according to the above-mentioned schemes is proposed. Also, this paper presents the analysis and comparative studies from the standpoint of stability, the volume of public and private keys, length of ciphertext and relative speed of information transmission of the new proposed scheme and McEliece and Niederreiter cryptosystems. It is considered from an analytical point of view and with the help of graphic images. Comparative studies revealed that the hybrid cryptosystem retains the positive aspects of its predecessors, as well as allows us to increase the relative transmission rate with the preservation of the stability indicator to the classical and quantum cryptanalysis. One disadvantage is the increase in decoding time by adding information extracted as in Niederreiter scheme, but the increase in this indicator is not critical. Despite the demonstrated benefits, it remains open to all cryptosystems to reduce the amount of the used key data, which, in the case of quantum computers to maintain stability, still needs to be increased once.
Highlights
A vast majority of modern cryptographic systems are based on mechanisms which provide protection due to the complexity of solving a particular mathematical problem such as discrete logarithm, factorization, etc. [1,2]
The high speed of cryptography and the resistance to classical and quantum cryptanalysis are distinguished by codebased systems from their competitors [5]
Taking into account the proved stability of the considered cryptosystems, we propose a new hybrid cryptosystem, which has the same advantages as its predecessors, and even improves their performance
Summary
A vast majority of modern cryptographic systems are based on mechanisms which provide protection due to the complexity of solving a particular mathematical problem such as discrete logarithm, factorization, etc. [1,2]. Cryptosystems based on coding are not currently widely used, but in the near future everything can change radically This change is due to the desire of the world community to create a full-scale quantum computer, which will be able to accelerate the performance of usual computer operations in dozens or even hundreds of times [3]. With this in mind, research into the postquantum cryptography, cryptography representing algorithms that are resistant to quantum and classical cryptanalysis, became relevant. Additional significant benefits that will be considered in the future
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