Re: Concerning Cryptography

From: Walter Roberson (roberson@ibd.nrc.ca)
Date: 01/24/02


From: roberson@ibd.nrc.ca (Walter Roberson)
Date: 24 Jan 2002 20:46:46 GMT

In article <f16f0b2a.0201231752.43e08d8e@posting.google.com>,
Peanut Butter <ISBN0111110@aol.com> wrote:
:I was wondering if someone could tell me all of the fields of
:mathematics incloved with cryptography so I can read up on those
:fields. Thank You.

Not really. Cryptography is a pretty big topic, and people keep
finding new ways of applying mathematics in order to impliment new
cryptography schemes or break old schemes.

Someone suggested you start with Discrete Mathematics. I would
disagree: I think you should start *way* before that. In particular,
I think you would not be able to understand Cryptography properly until
you understand these (and more!):

- elementary matrix operations -- matrix multiply, matrix inversions,
  solutions to simultaneous linear equations
- elementary set theory
- basic function theory. Composition of functions
- The Counting Argument
- basic probability and statistics theory -- conditional probabilities,
  mean, standard deviation
- integration and differentiation (otherwise you won't be able to do
  proper density functions for the statistics)
- introductory graph theory
- basic linguistic analysis
- modular arithmetic
- basic group and field theory
- introductory theory of computation. Turing machines. Finite Automata,
  Finite state machines