Comparative characteristics of Crystals-Kyber and Skelya key encapsulation algorithms (DSTU 8961-2019)

In recent years, there has been a significant amount of research related to the development of quantum computers. If such a computer were to be built, it would be able to break existing public-key cryptosystems that are currently used for many purposes. This will seriously affect the privacy and integrity of digital communications, etc. That is why special attention is currently being paid to post-quantum cryptography, the main goal of which is the development of cryptographic systems that are protected from both quantum and classical attacks, and will also be able to interact with existing communication protocols and networks. In view of the significant importance of the practical application of directional encryption algorithms, at the international and state level, special attention was paid to the implementation of the proposed requirements for key encapsulation protocols. Key-establishment algorithms (KEA) form a common secret – the key for a symmetric encryption algorithm. The paper considers two KEA algorithms that use algebraic lattices: one of the finalists of the 3rd round Crystals-Kyber and the Skelya algorithm (DSTU 8961-2019). The Kyber algorithm first performs asymmetric encryption of a 32-byte message, and then generates a shared secret. The Skelya algorithm performs the same actions, but for asymmetric encryption, it uses messages of any length that do not exceed the maximum possible. That is why the last algorithm can be used not only as a KEA algorithm, but also as an asymmetric encryption algorithm. According to the NIST Security level, the Kyber algorithm provides cryptographic 1, 3, and 5 security levels, and the Rock algorithm provides cryptographic 3, 5, and 7 security levels. The cryptographic stability that is ensured for both algorithms is determined by a set of parameters. Thus, the purpose of this work is to review the details of the implementation of each of the mentioned algorithms, to compare the speed of the key generation, encapsulation and decapsulation algorithms for the Kyber and Skelya algorithms in terms of key data lengths, and the encapsulation result and computational complexity of both algorithms.