Nelasa G. Improvement of methods of transformation in jacobians of hyperelliptic curves for cryptographic applications

The thesis is devoted to improvement of transformation methods on hyperelliptic curves, and to estimate features and future trends of using hyperelliptic curves arithmetic in cryptographic protocols with taking into account resistance and complexity requirements. The model of asymmetric transformations in jacobians of hyperelliptic curves obtains the further development. The method of scalar multiplication on elliptic and hyperelliptic curves with precomputation has been improved. Its efficiency is caused by simultaneous use of multisequencing of computational process and by exception of operations of doubling in zero windows. In the work the method of Hasse-Witt matrix elements for hyperelliptic curves of a special kind of any genus calculation has been improved by means reduction of calculations to computation of binomial coefficients.