Protecting Information: From Classical Error Correction to Quantum Cryptography

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.

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.