# What are some different cryptography methods?

Some of the most effective cryptography methods and algorithms are based of factoring large prime numbers (e.g. RSA). I'm curious whether there are some other cryptography methods. Somethings that is very mathematical or physical based. Of course, I know about quantum cryptography, but I'm interested in other things also. For example, braid groups which have connection to knot theory can have application in cryptography. What I am asking is for a similar thing. I mean, is there any branch or equations in mathematics or physics that can lead to a cryptography methods.

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Elliptic curves and chaos theory are among the answers IMHO. – Mok-Kong Shen Feb 3 '13 at 16:20
Lattice assumption became very cool recently. cs.ut.ee/~lipmaa/crypto/link/public/lattice – AntonioFa Feb 3 '13 at 17:08

For symmetric crypto, the theory of boolean functions can explain how the functions inside Feistel Networks or substitution permutation network are chosen. This yields connexions with coding theory and of course with finite fields of size $2^n$.
Pedantically, the cryptographic hardness comes from the representation of group elements, not the structure of the group. For example, all cyclic groups have the same structure (that of addition mod $n$). The natural representation of $(\mathbb{Z}_{p-1}, +)$ and the natural representation of $(\mathbb{Z}_p^*, \times)$ have very different cryptographic properties though they are isomorphic groups. – Mikero Mar 9 '13 at 3:33