Cryptography

ISBN-13: 9783319948171 / Angielski / Miękka / 2018 / 259 str.

Simon Rubinstein-Salzedo

Opis

This text studies cryptography from its earliest roots (2000 years ago), to the main cryptosystems used today for secure online communication. Many topics covered - originate from number theory, combinatorics, probability, and abstract algebra. The book is partitioned into three sections; the first part discusses classical ciphers and their cryptanalysis. The second - focuses on modern public key cryptosystems: Diffie-Hellman, ElGamal, RSA, and elliptic curve cryptography. This section analyzes attacks against these systems as well as attacks on the underlying math problems such as various clever factorization algorithms. Specialized topics such as zero knowledge proofs, cryptographic voting, coding theory, and new research are covered in the final section of this book.Aimed toward advanced high school students, undergraduates, and amateur mathematicians interested in cryptography, this book is suitable for independent study; - no prerequisites are assumed and it contains a large selection of problems, ranging from straightforward to -to difficult -that challenge the strongest students.

Recenzje

"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 a copy of this book within easy reach." (Mark Hunacek, MAA Reviews, January, 2019)

O autorze

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.

Blurb

This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication.

Beginning with classical ciphers and their cryptanalysis, this book proceeds to focus on modern public key cryptosystems such as Diffie-Hellman, ElGamal, RSA, and elliptic curve cryptography with an analysis of vulnerabilities of these systems and underlying mathematical issues such as factorization algorithms. Specialized topics such as zero knowledge proofs, cryptographic voting, coding theory, and new research are covered in the final section of this book.

Aimed at undergraduate students, this book contains a large selection of problems, ranging from straightforward to difficult, and can be used as a textbook for classes as well as self-study. Requiring only a solid grounding in basic mathematics, this book will also appeal to advanced high school students and amateur mathematicians interested in this fascinating and topical subject.