2 replies to this topic

[liamzebedee]

I was looking at the Diffie–Hellman key exchange algorithm and wondering, how would someone design something like that. Some insight thanks.

[WingedPanther]

Applied Mathematics.

The reality is that most encryption algorithms today are created and analyzed by mathematicians with a strong interest in programming and algorithms (pure logic, set theory, etc). Number Theory tends to be another branch that plays heavily into it.

[fayyazlodhi]

I would like to add that the requirement always comes from Computer Science or application itself and then mathematicians explore various of their domains to find solutions.

Some times the converse happens i.e. a mathematician finds an interesting application of his proof.

For instance, asymmetric key cryptography or public key cryptography as it is better known originates from the idea that we need to find a function whose inverse function is nearly impossible or computationally very expensive to compute. For e.g. RSA is based upon the assumption that it is difficult to factor a large integer composed of two or more large prime factors. If this assumption is weakened by some advancement in maths, RSA will no longer be secure.

A current research and new domain in cryptography is using Elliptic curve cryptography. The basic idea is that finding the discrete log of a random elliptic curve with respect to a base point is in computable. As of today it is expected to be the next generation of mathematics used to provide security on the internet.

ECC Tutorial