Formalization of statistical indistinguishability of probability distribution ensembles in Mizar

In recent years, formal verification applications have attracted significant attention. In particular, verification of the security of cryptosystems has been extensively investigated. In this study, we attempt to develop various mathematical libraries for cryptology using the Mizar proof checking system. Probability distribution is a fundamental principal of cryptology. We can define other cryptologic topics using our formalization of probability distribution. Currently, we are attempting to formalize the computational indistinguishability of probability distributions. In modern cryptology, the security of cryptographic systems is particularly defined by computational indistinguishability, which is known to be weaker than statistical indistinguishability. We introduce our formalized definitions of the statistical indistinguishability of probability distribution ensembles in Mizar. We then prove some formalized theorems concerning these definitions using the Mizar proof checker.