Cryptographic Mathematics Books


Once you have a good understanding of the background basics, you may want to further your studies with deeper insights into the mathematical and theoretical aspects of cryptography and security. The following books provide a more mathematically focused treatment of cryptographic algorithms.

  • A Course in Number Theory and Cryptography by Neal I. Koblitz . This mathematically intensive book introduces number theoretic concepts relevant to cryptography. No background in algebra or number theory is assumed, and the reader is methodically introduced to each important concept in a highly descriptive manner. Important algorithms are described along with an introduction to the analysis of complexity. This book also provides an introduction to the use of elliptic curves in cryptography, which is a rather advanced cutting-edge topic. Exercises and solutions are provided in each chapter.

  • The Mathematics of Ciphers: Number Theory and RSA Cryptography by S. C. Coutinho . This compact book (less than 200 pages) provides an easygoing introduction to relevant number theory and algorithms that pertain to RSA cryptography. It describes their relation to asymmetric encryption and works toward a good understanding of the RSA algorithm itself. The book takes you through many basic concepts, developing thorough understanding of how RSA works, which is described in its final chapter.

Learning about cryptographic mathematics is only the first step in gaining a thorough understanding of cryptographic theory. The second step is to learn about cryptanalysis, which is the task of analyzing and breaking existing ciphers. Generally, an understanding of cryptanalysis is not necessary for regular programmers who simply need to implement existing cryptographic algorithms into their applications. However, to design new algorithms, you must have a good grounding in modern cryptanalysis theory. Cryptanalysis is rather difficult, and it is virtually always simpler and safer to use existing, well- tested algorithms than to design your own. Thus, in almost all cases, algorithm design should be left to professional cryptographers. However, if you are interested in eventually becoming a professional cryptographer, or if you simply have a personal desire to learn as much as you can about cryptanalysis, then you should study the following books.

  • Differential Cryptanalysis of the Data Encryption Standard by Eli Biham and Adi Shamir . This is a mathematically advanced (you might even say scary) book that describes differential cryptanalysis as applied to the DES algorithm. It shows how to analyze the evolution of differences that result from related plaintexts that are encrypted using the same key. This technique is able to break the 16-round DES algorithm faster than any previously published attack. The same approach can be applied to some other symmetric algorithms as well.

  • Elementary Cryptanalysis: A Mathematical Approach by Abraham Sinkov . This explains, in an easy-to-understand manner, some fundamental approaches used in cryptanalysis. Topics covered include some statistics, modular arithmetic, simple number theory, and a smattering of linear matrix algebra.

  • Cryptanalysis: A Study of Ciphers and Their Solutions by Helen F Gaines . This book, which was published in 1939, is the bible of classical cipher analysis. Although classic ciphers are no longer seriously used today, making this book rather dated, it is still a very interesting read. It also provides many insights into the cryptanalysis mindset and gives you a feel for how cryptanalysis is planned and applied, without the bewildering mathematical complexity of modern cryptanalysis. It is also very interesting from a historical point of view.



.NET Security and Cryptography
.NET Security and Cryptography
ISBN: 013100851X
EAN: 2147483647
Year: 2003
Pages: 126

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