Cryptography, as done in this century, is heavily mathematical. But it also has roots in what is computationally feasible.
This unique textbook text balances the theorems of mathematics against the feasibility of computation. Cryptography is something one actually does, not a mathematical game one proves theorems about. There is deep math; there are some theorems that must be proved; and there is a need to recognize the brilliant work done by those who focus on theory. But at the level of an undergraduate course, the emphasis should be first on knowing and understanding the algorithms and how to implement them, and also to be aware that the algorithms must be implemented carefully to avoid the easy ways to break the cryptography. This text covers the algorithmic foundations and is complemented by core mathematics and arithmetic.

Balances the theorems of mathematics against the feasibility of computation Covers the algorithmic foundations as well core mathematics and arithmetic Demonstrates how cryptography is something one actually does, rather than theorizes about

Autorentext

Duncan Buell, emeritierter Professor im Fachbereich Informatik und Ingenieurwesen an der University of South Carolina, verfügt außerdem über 15 Jahre Erfahrung in einem Forschungslabor, das sich mit Hochleistungsrechnern für die US National Security Agency beschäftigt.

Klappentext

Cryptography, as done in this century, is heavily mathematical. But it also has roots in what is computationally feasible. This unique textbook text balances the theorems of mathematics against the feasibility of computation. Cryptography is something one actually "does", not a mathematical game one proves theorems about. There is deep math; there are some theorems that must be proved; and there is a need to recognize the brilliant work done by those who focus on theory. But at the level of an undergraduate course, the emphasis should be first on knowing and understanding the algorithms and how to implement them, and also to be aware that the algorithms must be implemented carefully to avoid the "easy" ways to break the cryptography. This text covers the algorithmic foundations and is complemented by core mathematics and arithmetic.

Inhalt

1. Introduction.- 2. Simple Ciphers.- 3. Divisibility, Congruences, and Modular Arithmetic.- 4. Groups, Rings, Fields.- 5. Square Roots and Quadratic Symbols.- 6. Finite Fields of Characteristic 2.- 7. Elliptic Curves.- 8. Mathematics, Computing, and Arithmetic.- 9. Modern Symmetric Ciphers DES and AES.- 10. Asymmetric Ciphers RSA and Others.- 11. How to Factor a Number.- 12. How to Factor More Effectively.- 13. Cycles, Randomness, Discrete Logarithms, and KeyExchange.- 14. Elliptic Curve Cryptography.- 15. Quantum Computing and Cryptography.- 16. Lattice-Based Cryptography.- 17. Homomorphic Encryption.- 18. Exercises.