
Mathematical Cryptology [pdf] - christianbryant
http://math.tut.fi/~ruohonen/MC.pdf
======
christianbryant
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](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.

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

~~~
ReidZB
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
'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/](http://jda.noekeon.org/)

[2]
[https://www.springer.com/computer/security+and+cryptology/bo...](https://www.springer.com/computer/security+and+cryptology/book/978-3-642-17341-7)

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

~~~
ReidZB
Thanks for the references! Especially Washington's work. I haven't studied it
before, but from a quick glance at the TOC, it looks like it's far more
complete than the one cited above.

