Kotukh Y. Methods and means of universal hashing by algebraic Suzuki curves

The thesis is devoted to solution of important scientific and technical problem, which consists in the development of the methods and means of universal hashing by the rational functions of Suzuki curves to build authentication scheme with provable security to ensure the guaranteed probability of collision with reduced computational complexity. Method of universal hashing based on rational functions of the Suzuki curve and the method of hash function computing based on Horner multiparameter scheme were developed. Functional field for curves associated with subgroups of the Suzuki group over the finite field with arbitrary power of expansion was built. The parameters of algebraic Suzuki curves over finite fields were estimated. The complexity of hash code computing and key space for universal hashing on Suzuki curve were obtained.