Koblitz's Improved Probability Mapping Method in the Elliptic Curve Cryptosystem: A comparative study and results

The cryptography using ECC remains mysterious and incomprehensible for most. This article provides basic knowledge and methods for understanding elliptic curve cryptography. The central thrust of this paper is to present an improvement of the Koblitz probabilistic mapping method using an example of a message written in Unicode Tifinagh characters; the modification focuses on the variables of its coding algorithm to make it easier to find the square roots of the EC equation corresponding to the mid blocks of message M. To confirm the effectiveness of the proposed algorithm, we compared it with two methods, one based on a generator point G of a subgroup of EC and a matrix to change the position of the points. and the second uses a hybrid ECC code scheme encoded by DNA. The experimental results of the comparison showed that the modified Koblitz mapping algorithm requires much less coding time, and that the coding time does not necessarily vary with the size of the message M. These results can increase the mapping speed as well as reduce energy consumption for cryptosystems based on EC.