DEVELOPMENT OF CRYPTOCODE CONSTRUCTIONS BASED ON ALGEBRAIC, LDPC, AND DAMAGE CODES
DOI:
https://doi.org/10.28925/2663-4023.2025.31.1061Keywords:
Rao-Nam crypto-code constructions, algebraic codes, LDPC, and defective codes.Abstract
The development of post-quantum technologies calls into question the cryptographic strength of modern symmetric and asymmetric cryptosystems. With the advent of a full-scale quantum computer, such systems will not be able to provide the required level of cryptographic strength (level 5 according to the US NIST scale). The competition of post-quantum algorithms has revealed a tendency towards the construction of cryptosystems based on the synthesis (integration) of security theories with Galois theory. Among the winners of post-quantum algorithms are the crypto-code constructions (CCC) of McEliece and Niederreiter, which make it possible to comprehensively provide the necessary level of protection and increase the level of probability of information transfer. But a significant drawback is the possibility of hacking such systems using linear codes, as well as the need to build them on the Galois field 210–213, which significantly reduces their ability to build systems based on intelligent technologies and mesh networks. The work proposes the use of symmetric CCC (SCCC) based on the Rao-Nama scheme (SCCC R-N) on MEC (modified elliptic codes), LDPC, and damage codes, which makes it possible to significantly reduce the volume of key data (constructing CCC using the Galois field 24–26) while maintaining the level of cryptographic strength of the probability of information transmission (the safe time is equal to the execution time of 1025–1035 elementary group operations). This approach makes it possible to create intelligent information security systems (ISPS). The purpose of the research is to develop post-quantum algorithms based on the integration of theories for constructing cryptosystems of symmetric and asymmetric cryptography with methods for constructing error-resistant codes. This approach allows you to regulate the required level of stability of the cryptosystems based on the requirements for the secrecy of the information message, as well as the time it is stored, and the level of stability of the system as a whole.
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