[DJVU] [2001] A Course in Number Theory and Cryptography (Gradua torrent

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BOOK INFO:

A Course in Number Theory and Cryptography (Graduate Texts in Mathematics)
By Neal Koblitz

Publisher: Springer-Verlag New York Inc.
Number Of Pages: 235
Publication Date: 2001-05
Sales Rank: 54940
ISBN / ASIN: 0387942939
EAN: 9780387942933
Binding: Hardcover
Manufacturer: Springer-Verlag New York Inc.
Studio: Springer-Verlag New York Inc.
Average Rating: 4.5
Total Reviews: 3





Date: 1999-09-02 Rating: 4
Review:

Cryptographer\'s toolbox

Two areas of this book deserve special mention. The first chapter develops a careful treatment of the _exact_ bit complexity of operations on numbers, such as +,-,*,/, modular powering, and gcd. While other books give crude estimates, or leave out such details entirely, Koblitz invests a good deal of time not only in giving the number of operations, but in teaching the reader how to make his own estimates. *Highly* useful.

Second, the book contains a concise introduction to modern factoring algorithms. After a discussion of primality testing, it goes on to develop the notion of a \"B-smooth\" number and then show how this leads to algorithms which use factor bases. Examples are given in the text, and the reasons behind that funny-looking time estimate O(e^(c*sqrt(log n log log n)) are provided. Seriously good stuff.

The exercises are also first rate - fun, intriguing, and serve to teach new ideas (not just test knowledge of the chapter).

In parts it shows its age (1994); for example, the Chor-Rivest knapsack described on p.115 has been broken by Serge Vaudenay. Much more discussion of randomized cryptography would also have been nice (though perhaps much in an intro book?). The most glaring deficiency is the lack of any real discussion of chosen ciphertext attacks, signature forgery, or padding schemes. You can\'t use this by itself to develop a new real-world project.

Instead, it\'s more like a \"cryptographer\'s toolbox,\" which gives you a thorough introduction to the primitives involved, giving you the understanding necessary to start thinking intelligently about how they are used.



Date: 1999-05-27 Rating: 5
Review:

Absolutely astounding!

Perfect. It gives the reader far more than what they expect in a wonderful manner. Highly recommended to anyone who has seen some Abstract Algebra.



Date: 1996-10-05 Rating: 4
Review:

Practical Tools

At a time when POP, as in POP-Maths, POP-Science etc, floods book-seller\'s shelves; it is clear that everyone wants quick results: Ah, yes: The new superman, Corporate, Tan and with a conversational knowledge of the generalised number sieve. Even the professional is drawn into this, producing books which give results: This is why Godel is important...this is what Diffie and Hellman did. The problem with propogating this tendency is that it suppresses an ability to engage with the METHODS used by the authors of these giant leaps: These methods are what will make up a readers toolbox for applying these theories more broadly. Cryptography, even at a professional maths level, is full of similar tendencies, books either give pseudo-political histories in a neurotic attempt at justifying their existence or they reflect the authors mathematical proclivities with respect to particular applications of number theory. Too much method and the wrong context. Neal Koblitz\'s book gives the methods AND results: Just enough to allow you to engage actively with the developments in the field. I was inspired and have great respect for his dedication of the royalties of this book to victims of US agression in America and South-East Asia. This is the kind of context we want. read this book. Sincerely Justin Arbuckle