Homomorphic Signature With Designated Evaluator

Homomorphic signature scheme with a designated evaluator extends traditional signature schemes by allowing only a specified entity to perform homomorphic operations on the signatures. However, existing schemes of this type are restricted to linear computations in their homomorphic evaluations, limiting their applicability in broader contexts. In this paper, we propose the first generic construction of a homomorphic signature scheme with a designated evaluator that supports arbitrary polynomial computations in its homomorphic evaluations. Technically, our construction leverages functional commitment schemes capable of arbitrary (polynomial) computations, combined with linear homomorphic signature schemes. Additionally, we achieve a post-quantum variant of this homomorphic signature scheme with a designated evaluator, provided that the underlying building blocks are post-quantum secure. This represents the first post-quantum realization of such a scheme.