A more efficient leveled strongly-unforgeable fully homomorphic signature scheme

Abstract Homomorphic signatures (HS) allow anyone to perform arbitrary efficient computation on signed data, whose output can be verified using the corresponding public verification key, without needing to have the underlying data. Existing HS schemes (e.g., Gorbunov et al., 2015; Fiore et al., 2016) are however inefficient in generating signatures, due to the fact that the signing algorithm can only generate one signature for an individual message at a time. In this work, we propose a new leveled fully homomorphic signature scheme, which only needs to call the signing algorithm twice for generating signatures for all messages in a dataset. This is a significant improvement in efficiency over the previous HS schemes that need to call the signing algorithm for polynomial times. We achieve this by using a vector encoding technique, which encodes all messages in a dataset into two matrices. Furthermore, we prove that our construction is secure against fully adaptive chosen-message attacks under the standard small integer solution (SIS) assumption.