[1] The CDH assumption involves the problem of computing the discrete logarithm in cyclic groups.
The CDH problem illustrates the attack of an eavesdropper in the Diffie–Hellman key exchange[2] protocol to obtain the exchanged secret key.
The CDH assumption states that, given for a randomly chosen generator g and random it is computationally intractable to compute the value The CDH assumption is strongly related to the discrete logarithm assumption.
If computing the discrete logarithm (base g ) in G were easy, then the CDH problem could be solved easily: Given one could efficiently compute
in the following way: Computing the discrete logarithm is the only known method for solving the CDH problem.
It is an open problem to determine whether the discrete log assumption is equivalent to the CDH assumption, though in certain special cases this can be shown to be the case.
There are concrete constructions of groups where the stronger DDH assumption does not hold but the weaker CDH assumption still seems to be a reasonable hypothesis.