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An Introduction To Cryptography
by Johannes Buchmann
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"This book is aimed at a broad audience. It preassumes very little knowledge of mathematics, gives a clear and systematic introduction into the subject whose popularity is ever increasing, and can be recommended to students and all people who would like to learn about cryptography. The book contains many exercises and examples. It can be used as a textbook and is likely to become popular among students. The necessary definitions and concepts from algebra, number theory and probability theory are formulated, illustrated by examples and applied to cryptography."
"[......] Of the three books under review, Buchmann's is by far the most sophisticated, complete and up-to-date. It was written for computer-science majors - German ones at that - and might be rough going for all but the best American undergraduates. It is amazing how much Buchmann is able to do in under 300 pages: self-contained explanations of the relevant mathematics (with proofs); a systematic introduction to symmetric cryptosystems, including a detailed description and discussion of DES; a good treatment of primality testing, integer factorization, and algorithms for discrete logarithms, clearly written sections describing most of the major types of cryptosystems, and explanations of basic concepts of practical cryptography such as hash functions, message authentication codes, signatures, passwords, certification authorities, and certificate chains. This book is an excellent reference, and I believe that it would also be a good textbook for a course for mathematics or computer science majors, provided that the instructor is prepared to supplement it with more leisurely treatments of some of the topics."
N. Koblitz (Seattle, WA) - American Math. Society Monthly.
From the reviews of the second edition:
"Cryptography is a key technology in electronic security systems … . This has led to the publication of many books that offer an introduction to cryptography, and its mathematical background. One of the most successful of these books is the one whose second edition is here under review. … The book is extremely well written and can be used as a textbook or for individual study. … The second edition includes updates and some new material." (S. C. Coutinho, The Mathematical Gazette, Vol. 90 (517), 2006)
Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control, and so forth. Users therefore should not only know how its techniques work, but they must also be able to estimate their efficiency and security. Based on courses taught by the author, this book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge who are interested in modern cryptographic algorithms and their mathematical foundation. Several exercises are included following each chapter. This revised and extended edition includes new material on the AES encryption algorithm, the SHA-1 Hash algorithm, on secret sharing, as well as updates in the chapters on factoring and discrete logarithms. Johannes A. Buchmann is Professor of Computer Science and Mathematics at the Technical University of Darmstadt, and an Associate Editor of the Journal of Cryptology. In 1985, he received a Feodor Lynen Fellowship of the Alexander von Humboldt Foundation. He has also received the most prestigious award in science in Germany, the Leibniz Award of the German Science Foundation (Deutsche Forschungsgemeinschaft).
A text written for students with only basic mathematical knowledge interested in the science of cryptography. Explains the basic methods, showing how to crack electronic codes, how to measure the efficiency and security of a code, and understand the basic techniques. DLC: Coding theory.
About the Author
Johannes A. Buchmann is Professor of Computer Science and Mathematics at the Technical University of Darmstadt, and an Associate Editor of the Journal of Cryptology. In 1985, he received a Feodor Lynen Fellowship of the Alexander von Humboldt Foundation. He has also received the most prestigious award in science in Germany, the Leibniz Award of the German Science Foundation (Deutsche Forschungsgemeinschaft).
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