Protecting Information
From Classical Error Correction to Quantum Cryptography

This book addresses protecting information from noise and eavesdropping by covering error correction and cryptography.

Susan Loepp (Author), William K. Wootters (Author)

9780521534765, Cambridge University Press

Paperback, published 31 July 2006

304 pages, 14 tables 159 exercises
23.5 x 15.8 x 1.5 cm, 0.43 kg

'The authors have combined the two 'hot' subjects of cryptography and coding, looking at each with regard to both classical and quantum models of computing and communication. These exciting topics are unified through the steady, consistent development of algebraic structures and techniques. Students who read this book will walk away with a broad exposure to both the theory and the concrete application of groups, finite fields, and vector spaces.' Ben Lotto, Vassar College

For many everyday transmissions, it is essential to protect digital information from noise or eavesdropping. This undergraduate introduction to error correction and cryptography is unique in devoting several chapters to quantum cryptography and quantum computing, thus providing a context in which ideas from mathematics and physics meet. By covering such topics as Shor's quantum factoring algorithm, this text informs the reader about current thinking in quantum information theory and encourages an appreciation of the connections between mathematics and science.Of particular interest are the potential impacts of quantum physics:(i) a quantum computer, if built, could crack our currently used public-key cryptosystems; and (ii) quantum cryptography promises to provide an alternative to these cryptosystems, basing its security on the laws of nature rather than on computational complexity. No prior knowledge of quantum mechanics is assumed, but students should have a basic knowledge of complex numbers, vectors, and matrices.

1. Cryptography: an overview
2. Quantum mechanics
3. Quantum cryptography
4. An introduction to error-correcting codes
5. Quantum cryptography revisited
6. Generalized Reed-Solomon codes
7. Quantum computing
Appendix.

Subject Areas: Algorithms & data structures [UMB], Quantum physics [quantum mechanics & quantum field theory PHQ], Coding theory & cryptology [GPJ]