Additive-Homomorphic Functional Commitments and Applications to Homomorphic Signatures

Functional Commitments (FC) allow one to reveal functions of committed data in a succinct and verifiable way. In this paper we put forward the notion of additive-homomorphic FC and show two efficient, pairing-based, realizations of this primitive supporting multivariate polynomials of constant degree and monotone span programs, respectively. We also show applications of the new primitive in the contexts of homomorphic signatures: we show that additive-homomorphic FCs can be used to realize homomorphic signatures (supporting the same class of functionalities as the underlying FC) in a simple and elegant way. Using our new FCs as underlying building blocks, this leads to the (seemingly) first expressive realizations of multi-input homomorphic signatures not relying on lattices or multilinear maps.