Generic algorithms for the discrete logarithm problem

This can be a significantly harder problem. For example, say we are using a randomized (Las Vegas) algorithm. If β lies in 〈α〉 then we are guaranteed to eventually find logα β, but if not, we will never find it and it may be impossible to tell whether we are just very unlucky or β 6∈ 〈α〉. On the other hand, with a deterministic algorithm such as the baby-steps giant-steps method, we can unequivocally determine whether β lies in 〈α〉 or not. There is also a generalization called the extended discrete logarithm: