Protecting Information: From Classical Error Correction to Quantum Cryptography

by Susan Loepp, William K. Wootters

Overview

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.

Product Details

ISBN-13:	9780521534765
Publisher:	Cambridge University Press
Publication date:	07/31/2006
Edition description:	New Edition
Pages:	304
Product dimensions:	6.22(w) x 9.25(h) x 0.59(d)

About the Author

Susan Loepp is an Associate Professor of Mathematics in the Department of Mathematics and Statistics at Williams College. Her research is in commutative algebra, focusing on completions of local rings.

William K. Wootters, a Fellow of the American Physical Society, is the Barclay Jermain Professor of Natural Philosophy in the Department of Physics at Williams College. He does research on quantum entanglement and other aspects of quantum information theory.

Table of Contents

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.

Editorial Reviews

"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

From the Publisher