Is there an efficient mathematical algorithm for Decision Diffie-Hellman problem in a finite field $F_q$? I have found a detailed analysis of many more involved or specific cases but nothing on the general finite field in which it must have been initially considered.
Thanks for your help.
First, note that DDH is defined over a group, not a field.
There are groups where DDH is easy. There are also groups where DDH is hard, almost as hard as DLP (discrete log problem).
At the moment, no, there is not a general algorithm for solving DDH in a general group. Only efficient algorithms for solving DDH in certain groups.