Generic Construction of Chameleon Hash to Group Elements

—Chameleon hash functions are trapdoor one-way functions with many applications such as chameleon signatures and on-line/off-line signatures. Previous research focused on the concrete constructions based on different assumptions, as well as schemes without the key-exposure problem. In this paper, we consider the structure-preserving schemes where messages, hash value and public keys all consist of elements of a group over which a bilinear map is efficiently computable. This property makes them useful in cryptographic protocols as they can nicely compose with other algebraic tools (like the GrothSahai proof systems). We first propose a concrete structurepreserving chameleon hash from a one-time linearly homomorphic Structure-Preserving Signature (SPS), without the keyexposure free property. Then, we give a generic construction of chameleon hash from any linearly homomorphic SPS satisfying a certain template, and key-exposure freeness can be achieved when full-fledged linearly homomorphic SPS is used.