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Title | Algebraic Aspects of Cryptography (Algorithms and Computation in Mathematics, Vol 3) |

Author(s) | Neal I. Koblitz |

ISBN | 3540634460 |

Language | English |

Published | January 1998 |

Publisher | Springer Verlag |

When certain technical people find out that I am involved in data security, they assert an interest in cryptography, and an intention to write a cryptographic program sometime. While I not wish to disparage this goal, questioning of the individual's background in mathematics tends to point out that the task is harder than they might have foreseen. The magic phrase "number theory" is usually the dividing line. For those who make it past that limit, I am going to recommend that they get Koblitz's work. Not that I am implying that this book is more demanding than it needs to be: only that the topic itself is a difficult one. This is the heart of cryptology: the underlying foundations that make it work. The material presented does not address specific programs, standards, or even algorithms, but deals with the basic mathematical theory that can be used to construct algorithms, or test their strength. Chapter one is something of an overview, touching on many fields of cryptography and introducing an appropriate and exemplar equation for each. Theories related to the strength of cryptographic algorithms are given in chapter two. Basic algebra associated with primes are discussed in chapter three, underlying the more common asymmetric (public key) systems such as RSA. Chapter four outlines an illustrative history of the development, cracking, and improvement of one particular algorithm, demonstrating the mathematical work necessary to each step. Knapsack type problems and theories are explained in chapter five. Chapter six deals with the currently very highly regarded elliptic curve algorithms, and is backed up with an even more extensive appendix on hyperelliptic curves. This is not an introduction. It is intended as a text for graduate (or possibly advanced undergraduate) work, and requires a solid background in mathematics or engineering. For those seriously interested in cryptography, though, it is worth the work. copyright Robert M. Slade, 2001

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