Short tightly secure signatures for signing a vector of group elements: A new approach

Abstract

We give a new approach to build tightly secure signatures for signing a vector of group elements in a bilinear group. We illustrate its usefulness to construct efficient signature schemes by giving two new constructions of partially structure preserving signature schemes, a weaker version of structure preserving signatures which are still compatible with Groth-Sahai Non-Interactive Zero-Knowledge Proofs. The first scheme is simpler to analyze, while the second scheme is more efficient and has a signature size of only 3 group elements. This is comparable to the state-of-the art in tightly secure signatures in bilinear groups without the partial structure preserving property. We finally give a third construction using the same ideas, a tightly secure signature scheme in bilinear groups which is comparable with the state-of-the-art.