On some connections between statistics and cryptology

The goal of this work is to describe some connections between cryptology and statistics. Starting from basic frequency analysis, throughout history, statistical ideas have been employed to attack cryptographic systems and continue to be important in modern day cryptanalysis. Brief descriptions of hypothesis testing based distinguishing attacks, differential cryptanalysis and statistical ideas used in side channel attacks are provided. From the designer's point of view, we consider three connections. A brief description is provided of the cryptographic ideas that have been suggested to strengthen the technique of randomised response. In recent times, a new notion of privacy of statistical databases has arisen and has been called differential privacy. We provide a brief description of this idea and mention some of its applications. Lastly, we consider the problem of defining and proving security of public key encryption schemes and provide a simple example of this method. It is hoped that the topics outlined here will motivate researchers to further investigate the connection between these two subjects.