I am writing a program for teaching security algorithms(such as DES, AES and
RSA), but writing the mathematical functions are very time consuming. Is
there any librarys for dealing with number theory? such as GCD, arbitrary
length integers, prime number generation, Fermat's and Euler's Theoerms,
Chinese remaninder theorem.

Something like BigNumber in Java and NTL. I know there is a cryptography
library in .NET framework, but it doesn't have the functons that I mentioned
before. I am using Visual Studio 2005 frofessional edition.
Anyone can help me?