Learning about cryptography requires examining fundamental issues about information security. Questions abound, ranging from “From whom are we protecting ourselves?” and “How can we measure levels of security?” to “what are our opponent’s capabilities?” and “What are their goals?” Answering these questions requires and understanding of basic cryptography. This book, written by Russian cryptographers, explains those basics. Chapters are independent and can be read in any order. The introduction gives a general description of all the main notions of modern cryptography: a cipher, a key, security, and electronic digital signature, a cryptographic protocol, etc. Other chapters delve more deeply into this material. The final chapter presents problems and selected solutions form “Cryptography Olympiads for (Russian) High School Students”. This is an English translation of a Russian textbook. It is suitable for advanced high school students and undergraduates studying information security. It is also appropriate for a general Mathematical audience interested in cryptography. Also on cryptography and available from the AMS is Codebreakers: Arne Beurling and the Swedish Crypto Program during World War II.

Main notions
Cryptograpy and complexity theory
Cryptographic protocols
Algorithmic problems of number theory
Mathematics of secret sharing
Cryptography olympiads for high school students
Bibliography