I'm curious about the relation between the Discrete Logarithm and Decisional Diffie-Hellman. Is it safe to have an assumption like the following to link the two?
Given uniformly and independently chosen g^x and g^y, if there is an efficient algorithm that can distinguish g^(xy) and random g^r with non-negligible probability, then there is an extractor that can extract x or y with non-negligible probability?
This looks like a Knowledge of Exponent assumption, however, I want it to tackle the decisional problem. Also it is known that some elliptic curve groups could use pairing to break DDH, in this case, we'll restrict the discussion to groups such as the group of Quadratic Residue over Blum integers.