Protecting Information: From Classical Error Correction to Quantum Cryptography

Description

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.

• Accessible to readers familiar with matrix algebra, vector spaces and complex numbers

 • First undergraduate text to cover cryptography, error-correction, and quantum computation together

 • Features exercises designed to enhance understanding, including a number of computational problems, available from www.cambridge.org/9780521534765

 

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.