Mathematical Cryptology [pdf]

http://math.tut.fi/~ruohonen/MC.pdf

by christianbryant • 12 years ago

37 5 12 years ago

math.tut.fi

FredericJ• 12 years ago

Anyone has other good crypto handbooks? I would be interested.

ReidZB2• 12 years ago

Mmm, certainly.

Hoffstein et al.'s An Introduction to Mathematical Cryptography is a wonderful text, highly thought of, that really is a better choice than the above link for this sort of thing. Another shorter text is Koblitz's A Course in Number Theory and Cryptography, but I think all of the material in that is also in Hoffstein et al.'s Introduction.

For a practical implementation-oriented treatment, Cryptography Engineering by Ferguson, Schneier, and Kohno is a good text. It's especially great as a launching point for someone interested in cryptography, especially from a systems-building perspective.

For a mostly-rigorous treatment of the basics and theory of modern cryptography, I am a huge fan of Katz and Lindell's Introduction to Modern Cryptography; I've espoused its virtues several times here on HN. If you want the theoretical background with some application still thrown in, this is a good choice.

For a deep theoretical treatment, requiring an already-built background in theoretical computer science and probability theory, see Goldreich's Foundations of Cryptography volumes. They are very dense, very dry works, but packed with information.

For a specific focus on elliptic curve cryptography, Menezes et al. have published Guide to Elliptic Curve Cryptography, though elliptic curves are also treated in the above two references (Hoffstein et al. and Koblitz). Still, I appreciate the focus on ECC, which is large enough to merit entire books.

For a reference text, Menezes et al.'s Handbook of Applied Cryptography contains a lot of information, although it's starting to show its age. Still, if you need to find a definition or something, it's a great place to look.

For an understanding of the (roughly) state-of-the-art in block ciphers, see Rijmen and Daemen's The Design of Rijndael. (Rijndael is perhaps better known as "AES" today, modulo some minor differences; Rijmen and Daemen are the creators of Rijndael).

For a treatment of the history of cryptology, the seminal work is Kahn's The Codebreakers. It is a massive text, but covers cryptologic history relatively well - up until recent times, anyway. For a shorter but still good text, see Singh's The Code Book.

Then, there are areas of mathematics and theoretical computer science that are used heavily in cryptography. The above already include some references to that (quite a few of the above text include an intro to number theory section, for example), but of course, there are always the textbooks designed specifically for that field. For instance, Dummit and Foote's Abstract Algebra, Baker's Comprehensive Course in Number Theory, Papadimitriou's Computational Complexity, and so on. Those are pretty easy to find with Google, though, if you search for influential textbooks in those fields.

This list is hopelessly incomplete, but I think it is quite a good broad survey of some different textbooks. If you studied all of the above in their entirety, you would be quite knowledgeable, at least.

Edit: Well, uh, here at 5am I realized you were probably talking about ones that were available online or what have you. Oops. Of the above, I think only the Handbook of Applied Cryptography is (legally) free. Still, I'll leave this here for future reference.

pbsd• 12 years ago

'The Design of Rijndael', plus errata, is available in Joan Daemen's page [1]. As an addition, 'The Block Cipher Companion' [2] is a more recent, less AES-centric, overview on block ciphers.

As for elliptic curves, I'm a fan of Washington's 'Elliptic Curves: Number Theory and Cryptography' [3], which contains a lot of detail while remaining readable. But it might not the best introductory material.

[1] http://jda.noekeon.org/

[2] https://www.springer.com/computer/security+and+cryptology/bo...

[3] http://www2.math.umd.edu/~lcw/ellipticcurves.html

christianbryant• 12 years ago

I came across this paper because I read the Journal of Universal Computer Science, of which he is the current editor: http://www.jucs.org/jucs

In particular, because quantum cryptology is an area I am reading in right now, I thought Keijo's breakdown was very understandable.

Mathematical Cryptology [pdf]

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