"A Course in Number Theory and Cryptography" by Neal Koblitz is a textbook that introduces both classical and modern topics in number theory and cryptography. It is designed for students with little or no background in algebra or number theory. The book emphasizes algorithmic approaches and the efficiency of techniques, with a special focus on the application of elliptic curves in cryptography. It includes extensive exercises to help readers understand the material. The first two chapters provide a general background in number theory and finite fields. While the exposition is condensed, readers with no prior exposure to algebra or elementary number theory are advised to consult more leisurely textbooks for details. Those with more mathematical background may skim through these chapters. The book is structured to cover most of the first five chapters in a semester, or to serve as a sequel to a one-semester course in elementary number theory, covering Chapters III–VI. The chapters are organized to build upon each other, with some references to earlier chapters in Chapters V and VI. The book is based on courses taught at the University of Washington and the Institute of Mathematical Sciences. The author thanks those who used the manuscript and provided helpful corrections. The frontispiece illustrates the theme of the book, with coded decimal digits along the walls of a building, not random. The book is dedicated to the memory of students in Vietnam, Nicaragua, and El Salvador who lost their lives in the struggle against U.S. aggression. The author's royalties will be used to buy mathematics and science books for universities and institutes in these countries. In the second edition, the book includes several corrections and clarifications, and adds new sections on zero-knowledge proofs, oblivious transfer, the quadratic sieve factoring method, and the use of elliptic curves for primality testing. It also includes brief discussions on various cryptographic concepts, such as k-threshold schemes, probabilistic encryption, hash functions, and the U.S. government's Digital Signature Standard. The second edition reflects the expansion of cryptography into new areas, including algebraic number theory and arithmetic algebraic geometry."A Course in Number Theory and Cryptography" by Neal Koblitz is a textbook that introduces both classical and modern topics in number theory and cryptography. It is designed for students with little or no background in algebra or number theory. The book emphasizes algorithmic approaches and the efficiency of techniques, with a special focus on the application of elliptic curves in cryptography. It includes extensive exercises to help readers understand the material. The first two chapters provide a general background in number theory and finite fields. While the exposition is condensed, readers with no prior exposure to algebra or elementary number theory are advised to consult more leisurely textbooks for details. Those with more mathematical background may skim through these chapters. The book is structured to cover most of the first five chapters in a semester, or to serve as a sequel to a one-semester course in elementary number theory, covering Chapters III–VI. The chapters are organized to build upon each other, with some references to earlier chapters in Chapters V and VI. The book is based on courses taught at the University of Washington and the Institute of Mathematical Sciences. The author thanks those who used the manuscript and provided helpful corrections. The frontispiece illustrates the theme of the book, with coded decimal digits along the walls of a building, not random. The book is dedicated to the memory of students in Vietnam, Nicaragua, and El Salvador who lost their lives in the struggle against U.S. aggression. The author's royalties will be used to buy mathematics and science books for universities and institutes in these countries. In the second edition, the book includes several corrections and clarifications, and adds new sections on zero-knowledge proofs, oblivious transfer, the quadratic sieve factoring method, and the use of elliptic curves for primality testing. It also includes brief discussions on various cryptographic concepts, such as k-threshold schemes, probabilistic encryption, hash functions, and the U.S. government's Digital Signature Standard. The second edition reflects the expansion of cryptography into new areas, including algebraic number theory and arithmetic algebraic geometry.