Is there an efficient solution? Finding the number of matching items in lists with a threshold Alice and Bob both have a list of n items. They want to know the number of items that are occurring in both lists. The catch is, that they should receive 0/no result as a result if less than k items occur in both lists. If more than k items occur in both lists, they can learn anything from each other.

I think this can be done by generating all possible subsets of k items and multiplying the hashes of the items in the subsets with the generator point on an elliptic curve.
Then all resulting points for Alice and Bob for all subsets could be compared.

However, that solution would grow exponentially with k. Is there a better solution to solve this problem?
There has been work on finding the size of the set intersection. I haven't read this paper, but this would be a good place to start your research: Fast and Private Computation of Cardinality of Set Intersection and Union.