How does the elliptic-curve version of Diffie-Hellman cryptography work?

The basic principle is the same, but the selection of the private key and how the public key are computed are significantly different. In addition, everyone has to agree beforehand on the elliptic curve to use.

The basic principle is the same, but the selection of the private key and how the public key are computed are significantly different. In addition, everyone has to agree beforehand on the elliptic curve to use. As noted, in the elliptic-curve version of Diffie-Hellman, you first decide which elliptic curve you're using.

That determines a number of independent parameters called the domain parameters. Without getting too technical, it turns out that some curves are better than others for cryptographic purposes, so the parameters are actually chosen carefully rather than at random. This is somewhat analogous to picking good prime factors.

There are two sets of domain parameters: E, the elliptic curve itself. G, a point on E that is called the base point. E and G are necessary and sufficient to describe all the information you need.In ECC-DH, the private key d is computed by taking a randomly selected number on the interval 1, n-1, where n is the order of G.

The public key Q is computed by taking Q = dG. After that the general idea is the same, except that instead of trying to solve a hard integer factorization problem, you're trying to solve a hard discrete logarithm problem.

E is the identity element of the group... ow now I get it... In algebra, an identity or identity element of a set E with a binary operation · is an element e that, when combined with any element x of S, produces that same x. That is, e·x = x·e = x for all x in E. How does this apply to G^n of set E where set E is (y^2 = x^3 + ax + b) How do I get the base point?

How do I determine e, how do I solve n? – cmaduro Apr 23 '10 at 20:34 Unfortunately, elliptic-curve cryptography isn't a trivial subject. I'm not sure that a comment is enough to cover everything you ask as follow-up questions.

It might be better if you did a little research into the topic first, or at least know some group theory. Check out certicom. Com/index.

Php/ecc-tutorial for a decent intro. – John Feminella Apr 23 '10 at 20:42 Some people have suggested I forget this whole idea, and use SSL. I like to create my own solutions.

What a complicated solution this is proving to be. – cmaduro Apr 23 '10 at 21:14 1 Well, standard DH is also a discrete logarithm problem and not an integer factorization problem. And it also has domain parameters.

– GregS Apr 23 '10 at 0:39.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.