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Fundamentals of Cryptology

Henk C. A. van Tilborg, 2000, Kluwer Academic. 491pp., hardbound, CD-ROM.

Fundamentals of Cryptology is a fairly complete presentation of cryptography and cryptanalysis (in short, cryptology) as well as the underlying mathematics.  There are several chapters describing different crypto systems, their implementations, and known attacks or weaknesses, including well-known systems such as Caesar ciphers (with many variants, such as Vigenere), block ciphers (e.g., DES), public-key (e.g., discrete logarithm and RSA) as well as coding theory or knapsack based systems, etc.

Several chapters describe the different types of mathematics needed, such as shift register sequences, elliptic curves, finite fields, and number theory.

The whole book is authored in Mathematica and the corresponding notebook (yes, there is actually only one big notebook) comes on a CD-ROM. Everything in every example can be modified and played with, as every concept is worked out in Mathematica code. 

In the preface, van Tilborg writes, "The whole manuscript is electronically available as an interactive Mathematica manuscript. So, there are hyperlinks to other places in the text, but more importantly, it is now possible to work out non-trivial examples. Even a non-expert can easily alter the parameters in the examples and try out new ones. It is our experience, based on teaching at the California Institute of Technology and the Eindhoven University of Technology, that most students truly enjoy the enormous possibilities of a computer algebra notebook." (See Henk C. A. van Tilborg's web page.)

--Roger Germundsson (

This book is available from The Mathematica Bookstore.

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