Some specific category. In general, the best we know how to do is a square-root speed up, which would only be applicable here if the number of possible solutio

Some specific category. In general, the best we know how to do is a square-root speed up, which would only be applicable here if the number of possible solutions were 10^160. (Specific categories do appear to have marvelous exponential speed-ups, such as factoring.)