FOR PSEUDORANDOM SEQUENCES BASED ON ELLIPTIC CURVE ISOGENIES GENERATING METHOD

Abstract

The pseudorandom sequences generation is a cryptographic systems fundamental aspect that affects cryptographic strength. One of these sequences advanced generating methods involves the use of elliptic curves (ECs), in particular by exploiting the isogeny properties of ECs. This approach not only improves the security features of cryptographic algorithms, but also ensures efficiency and reliability in the generation process. The use of isogenic transformations - morphisms between elliptic curves that preserve their group structure - further enriches the technique by introducing complex algebraic operations that are difficult to solve. Recent research has detailed the effectiveness of pseudorandom sequence generators based on elliptic curves. Methods have been developed that exploit the properties of elliptic curves over finite fields to generate sequences with low correlation and high linear complexity. There is also another approach that uses linear shift feedback registers (LFSRs) in combination with elliptic curve points to generate pseudorandom sequences. The new obtained method makes it possible to increase the number of internal states of the Dual_EC_DRBG generator by √n times, where n is the number of cyclic subgroups of simple order of the initial curve. This increases the complexity of disclosing the law of formation of the DRBG by an attacker. The application of the developed method also allows to avoid the existing disadvantages of Dual_EC_DRBG The article investigates the use of EC isogenies in the generation of pseudorandom sequences, considering their potential for improving cryptographic strength. By means of a detailed analysis of the algebraic structure and properties of these transformations, a method for PSPs generating is developed that can potentially provide advantages over existing methods in terms of security and efficiency in the transition period to post-quantum cryptography.