Universal codes efficiently compress sequences generated by stationary and ergodic sources with unknown statistics, and they were originally designed for lossless data compression. In the meantime, it was realized that they can be used for solving important problems of prediction and statistical analysis of time series, and this book describes recent results in this area. The first chapter introduces and describes the application of universal codes to prediction and the statistical analysis of time series; the second chapter describes applications of selected statistical methods to cryptography, including attacks on block ciphers; and the third chapter describes a homogeneity test used to determine authorship of literary texts. The book will be useful for researchers and advanced students in information theory, mathematical statistics, time-series analysis, and cryptography. It is assumed that the reader has some grounding in statistics and in information theory.

This textbook describes the main techniques and features of contemporary cryptography, but does so using secondary school mathematics so that the concepts discussed can be understood by non-mathematicians. The topics addressed include block ciphers, stream ciphers, public key encryption, digital signatures, cryptographic protocols, elliptic curve cryptography, theoretical security, blockchain and cryptocurrencies, issues concerning random numbers, and steganography. The key results discussed in each chapter are mathematically proven, and the methods are described in sufficient detail to enable their computational implementation. Exercises are provided.

Universal codes efficiently compress sequences generated by stationary and ergodic sources with unknown statistics, and they were originally designed for lossless data compression. In the meantime, it was realized that they can be used for solving important problems of prediction and statistical analysis of time series, and this book describes recent results in this area. The first chapter introduces and describes the application of universal codes to prediction and the statistical analysis of time series; the second chapter describes applications of selected statistical methods to cryptography, including attacks on block ciphers; and the third chapter describes a homogeneity test used to determine authorship of literary texts. The book will be useful for researchers and advanced students in information theory, mathematical statistics, time-series analysis, and cryptography. It is assumed that the reader has some grounding in statistics and in information theory.