Applications Of The Markov Chain Monte Carlo Method In Cryptography

With the rapid development of information technology, the information securityproblems have been attracting more researchers’ attention. In this context, the paperstudies the application of the Markov chain Monte Carlo methods in the field ofcryptography. In short, the Markov chain Monte Carlo method is a very powerfulstochastic simulation method and widely used in various fields.This article mainly consists of two sections, the first section concerns the theoriesin statistics, which contains an introduction of the basic knowledge about cryptographyand the Markov chain Monte Carlo method. There is a brief introduction to the historyof the development of the Markov chain Monte Carlo method in this part. We focus ontwo typical Markov chain Monte Carlo methods, called Metropolis-Hastingsalgorithm and Gibbs sampling. Then we discuss the application of Markov chainMonte Carlo methods in the field of cryptography, especially the substitution cipher.After analyzing the process of using the classic Metropolis-Hastings algorithm tobreak substitution cipher, we design another algorithm using the Gibbs sampling to doit better. In the second section, we will get some conclusions from practicalapplications. Using the Java programming language, we write a program to deciphersubstitution cipher with the Gibbs sampling method. The program works very well ona32-bit laptop, and we use it to do statistical calculating. We also discuss the problemsabout convergence speed and convergence diagnosis of the algorithm. The results showthat the Gibbs sampling algorithm performed much better than the classic Metropolis-Hastings algorithm in breaking the substitution cipher. The new algorithm is faster andsaves computer resources.