Cryptography

The present book presents a good undergraduate introduction to cryptography from its earliest roots to contemporary cryptosystems. It also contains all the necessary mathematical background for its comprehension and a large selection of problems. (Dimitros Poulakis, zbMATH 1408.94001, 2019) There is certainly a lot of interesting mathematics to be learned here, and the reader will have fun learning it. If I were teaching a course in cryptography, this text would definitely be on my very short list; people teaching a course in number theory who want to discuss some cryptography might also want to keep acopy of this book within easy reach. (Mark Hunacek, MAA Reviews, January, 2019)

Simon Rubinstein-Salzedo received his PhD in mathematics from Stanford University in 2012. Afterwards, he taught at Dartmouth College and Stanford University. In 2015, he founded Euler Circle, a mathematics institute in the San Francisco Bay Area, dedicated to teaching college-level mathematics classes to advanced high-school students, as well as mentoring them on mathematics research. His research interests include number theory, algebraic geometry, combinatorics, probability, and game theory.

Introduction. -1. A quick overview. -2. Caesar ciphers. -3. Substitution ciphers. -4. A first look at number theory. -5. The Vigenre cipher. -6. The Hill Cipher. -7. Other types of ciphers. -8. Big O notion and algorithm efficiency. -9. Abstract Algebra. -10. A second look at number theory. -11. The Diffie-Hellman Cryptosystem and the Discrete Logarithm Problem. -12. The RSA Cryptosystem. -13. Clever factorization algorithms and primality testing. -14. Elliptic curves. -15. The versatility of elliptic curves. -16. Zero-Knowledge Proofs. -17. Secret sharing, visual cryptography, and voting. -18. Quantum Computing and Quantum Cryptography. -19. Markov chains. -20. Some coding theory. Bibliography. Index.