The Analysis and Investigation of Multiplicative Inverse Searching Methods in the Ring of Integers Modulo M

In this article an investigation into search operations for the multip licat ive inverse in the ring of integers modulo m for Error Control Coding tasks and for data security is shown. The classificat ion of the searching operation of the multip licat ive inverse in the ring of integers modulo m is provided. The best values of parameters for Joye-Paillier method and Lehmer algorithm were also found. The improved Bradley modification for the extended Euclidean algorithm is also offered, which g ives the operating speed improvement for 10-15%. The integrated experimental research of basic classes of searching methods for multiplicative inverse in the ring of integers modulo m is conducted for the first time and the analytical formulas for these calculations of random access memory necessary space when operated at k-ary RS-algorithms and their modifications are shown.