Computational Diffie-Hellman Assumption

The computational Diffe-Hellman (CDH assumption) is the assumption that a certain computational problem within a cyclic group is hard.
Consider a cyclic group G of order q. The CDH assumption states that, given (g,g^a,gb), fro a randomly chosen generator g and random a,b in {0,1,... q-1}, it is computationally intractable to compute the value g^(ab).
The security of many cryptosystems is based on the CDH assumption. Also the confidentiality of ELGamal encryption is equivalent to the CDH assumption (through the semantic security of the scheme is based on the decisional Diffie Hellman assumption.)
The CDH assumption is related to the discrete logarithm assumption, which holds that computing the discrete logarithm of a value base a generator g is hard. If taking discrete logs in G were easy, then the CDH assumption would be false: given (g,g^a,gb), one could efficiently compute g^(ab) in the following way:

• compute a by taking the discrete log of g^a to base g;
• compute g^(ab) by exponentiation: g^(ab) = (g^b)a;

It is an open problem to determine whether the discrete log assumption is equivalent to CDH, though in certain special cases this can be shown to be the case.