Use of recurrent sequences to construct cryptographic methods with the public key

Abstract

The paper shows a possibility of the use of recurrent sequences for constructing cryptographic methods with the public key. The method of distribution of secret keys via the open channel, on the basis of recurrent and -sequences and their relations, was presented. It could become a basis for the construction of cryptographic transformations with the public key for different purposes such as encryption, authentication or digital signature. A research of the presented method as regards cryptographic reliability and computational complexity was conducted. The research showed that the method has advantages over the known methods, for, given availability of the sufficient level of stability, it allows setting the desired cryptographic reliability depending on the parameter k. Regarding the computational complexity, in comparison with the known method of Diffie-Hellman, the proposed method provides for each user almost twice as low a computational complexity, but also has a simpler procedure of task parameters.