From Error Correction to Quantum Cryptography
WILLIAMSTOWN, Mass., Dec. 6, 2006 -- Mathematician Susan Loepp and physicist William K. Wootters share the secrets of cryptography, cryptanalysis, and error correction in their text book, "Protecting Information: From Classical Error Correction to Quantum Cryptography" (Cambridge University Press).
"Protecting Information" begins with a brief history of secret codes and goes on to explain important present-day cryptosystems as well as futuristic schemes based on the laws of quantum physics. A text for undergraduates, the book also introduces students to mathematical strategies used to ensure the faithful transmission of information through noisy channels.
"It's remarkable how many interesting ideas in math and physics fall naturally under the heading of protecting information," says Wootters. "These are ideas that are fun to think about in their own right, such as the strangeness of quantum entanglement or the alternative arithmetic of finite fields. It's an added bonus that they are also useful and relevant to our everyday life."
Information is vulnerable to interception, perhaps by an identity thief, or to corruption by perfectly innocent sources of noise such as a scratch on a CD.
For this reason communications are often protected by mathematical codes designed either to compensate for noise or to baffle a potential eavesdropper. But an eavesdropper of the future might have access to a powerful device called a "quantum computer," which could crack many of the codes we currently use. The book shows not only how a quantum computer could perform this feat, but also how its effects could be overcome with "quantum cryptography," a technique that is still in the experimental phase but is not far from practical implementation.
Loepp and Wootters emphasize the close relationship of their fields, pulling together ideas from the fields of mathematics, physics, and computer science, in the discussion of their subject.
The mathematics and physics sections build one on top of the other. "The book is constructed with the intention that these different facets complement and reinforce each other. Thus the mathematics and science are to some extent interwoven, not necessarily seamlessly but in such a way as to make use of the connections," write the authors.
Assuming students' prior exposure to linear algebra, the text opens with an overview of cryptography. Error-correcting codes and generalized Reed-Solomon codes each earn a chapter, as do quantum mechanics, quantum cryptography, and quantum computing.
Highlights include a description of the popular RSA public-key cryptosystem, and a detailed account of the algorithm by which a quantum computer could someday render this system useless.
Loepp is associate professor of mathematics and Wootters is the Barclay Jermain Professor of Natural Philosophy at Williams College.
Loepp received her B.A. from Bethel College and her Ph.D. in 1994 from the University of Texas at Austin. Her field of research is commutative algebra and she often teaches abstract algebra courses at Williams.
Wootters earned his B.S. from Stanford and his Ph.D. from the University of Texas at Austin. His research focuses on quantum information theory and the foundations of quantum mechanics. Among the courses he is teaching this year is a course on mathematical methods for scientists.
In collaborating on this book, Loepp and Wootters called on students in their Williams College course, "Protecting Information: Applications of Abstract Algebra and Quantum Physics," for suggestions, which are included in the book. The authors have used their teaching experience to try to anticipate the reader's questions and to answer them in the text.
"We incorporated student feedback into the book, which we believe substantially improved the final version," says Loepp.
Williams College is consistently ranked one of the nation's top liberal arts colleges. The college's 2,000 students are taught by a faculty noted for the quality of their teaching and research, and the achievement of academic goals includes active participation of students with faculty in this research. Students' educational experience is enriched by the residential campus environment, which provides a host of opportunities for interaction with one another and with faculty beyond the classroom. Admission decisions are made regardless of a student's financial ability, and the college provides grants and other assistance to meet the demonstrated needs of all who are admitted. Founded in 1793, it is the second oldest institution of higher learning in Massachusetts. The college is located in Williamstown, Mass. To visit the college on the Internet: www.williams.edu
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