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PROTECTING INFORMATION
For many everyday transmissions, it is essential to protect digital informa-
tion from noise or eavesdropping. This undergraduate introduction to error
correction and cryptography is unique in devoting several chapters to quan-
tum cryptography and puting, 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 think-
ing 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
puter, if built, could crack our currently used public-key cryp-
tosystems; and (ii) quantum cryptography promises to provide an alternative
to these cryptosystems, basing its security on the laws of nature rather than
plexity.
No prior knowledge of quantum mechanics is assumed, but students
should have a basic knowledge plex 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 muta-
tive algebra, focusing pletions 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.
“The authors bined the two ‘hot’ subjects of cryptography and cod-
ing, looking at each with regard to both classical and quantum models of
computing munication. 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 Colle