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Experimental Research of the Developed Methods of Arithmetic Operations in Cryptographic Transformations according to the ECDSA Scheme

The national PKI regulates the use of a qualified electronic signature according to the algorithms of DSTU 4145-2002, ECDSA, DSA and RSA. Operations of creating and verifying electronic signature are based on various mathematical methods: transformation in a ring of integers, field of integers and polynomials, in a group of points of an elliptic curve. All these transformations are impossible without arithmetic operations on integers. In this work authors presented experimental results for implementation previously proposed methods of integers representation with delayed carry form and methods of arithmetic operations on numbers in this representation for ES cryptographic transformations according to the ECDSA scheme. To test the proposed methods of ECDSA cryptosystem operations over a prime GF (p) field, two software collections were prepared – using 32-bit machine words, and using 64-bit machine words. To compare the obtained results, operations without the use of the proposed methods were used as a reference. The comparison was made by comparing the average execution time of 1 million iterations of operations in the software implementation. Based on the analysis results it can be concluded that the proposed methods are more effective than classical.