The Numerical Algorithm For The Linear Congruential Equations With Single Modulus / Multi-modulus And Its Application In Cryptography

Congruence equations is the numberical equations with variable coefficient being limited to certain finite fields the same type of finite fields leads to different types of equations, such as single congruence equation and multi-modulus linear congruential equations. Congruenceequations play an important role in information security, such as cryptography and other fields. It is that different types of problems presented in these areas leading to the rapid development of the solving theory of equations, making the solving of congruence equations become one of the most active and popular topics in both the field of mathematics and cryptography research. This master's thesis has studied a multi-modulus linear congruential equations and application problems, the major work done and results obtained are as follows:1 As for the problems to single linear congruential equations, Gauss method and the L U solution to the solving problems of single linear congruential equations is presented and the algorithm and numerical examples is given.2 As for the problems to multi-modular linear congruential equations, the Generalized Chinese Remainder Theorem and its applications is presented, the algorithm and numerical examples is given.3 Based on the generalized Chinese Remainder Theorem problems, A problem of multi-modulus linear congruential equations being an composite number and its application is proposed and the algorithm and numerical examples id given.4 As for multi-modular matrix, the solving inverse problems to the left and right inverse matrix of multi-modular matrix with the multi-modular being a composite number and their application is presented, and we can research and obtain the generalized multi-modulus Hill system, the algorithms and numerical examples are given.It makes solutions to these problems become easy by means of mathematical software.5 As for the problems to multi-modular linear equations, the encoding method to a multi-modulus linear congruential equations is proposed, the algorithm and numerical examples is given.