In this talk (which includes an extended introduction so that even non-cryptographers can follow along) we explore Homomorphic Signatures for NP (HSNP). HSNPs allow us to verify that a signed result is indeed the outcome of a specified (potentially complex) computation on signed inputs. This powerful notion was introduced by Fiore and Tucker at CCS 2022, where they combined zero-knowledge SNARKs (for succinct proof of correct computation) with linearly homomorphic signatures (LHS) to verify operations on streaming data. Although their approach was very flexible, the verification step of their LHS was quite costly. We address this limitation by introducing a new, more efficient LHS, significantly reducing the verification overhead. By retaining Fiore and Tucker’s modular design, our solution yields a streamlined HSNP, particularly advantageous for processing data that arrives in consecutive samples, such as sliding window statistics, histograms, and financial forecasts.