International Association
for Cryptologic Research

Fully homomorphic signatures are a significant strengthening of digital signatures, enabling computations on \emph{secretly} signed data. Today, we have multiple approaches to design fully homomorphic signatures such as from lattices, or succinct functional commitments, or indistinguishability obfuscation, or mutable batch arguments. Unfortunately, all existing constructions for homomorphic signatures suffer from one or more limitations. We do not have homomorphic signatures with features such as multi-hop evaluation, context hiding, and fast amortized verification, while relying on standard falsifiable assumptions.

In this work, we design homomorphic signatures satisfying all above properties. We construct homomorphic signatures for polynomial-sized circuits from a variety of standard assumptions such as sub-exponential DDH, standard pairing-based assumptions, or learning with errors. We also discuss how our constructions can be easily extended to the multi-key setting.