q-DLOG ⇒ Prime-order DLOG

Fully-black-box reduction · standard model · folklore · security loss: none: the reduction forwards the adversary’s answer

Statement

If $q$-DLOG is hard for a bilinear group generator, then DLOG is hard in prime-order groups for the generator that runs it and outputs $({\mathbb{G}}_1,g_1,p)$: a solver given $({\mathbb{G}}_1,g_1,p,g_1^x)$ is a $(1,1)$-DLOG solver that ignores $g_2^x$ and the rest of the bilinear group, with the same advantage — folklore.