Novel constructions of cramer-shoup like cryptosystems based on index exchangeable family

The Cramer-Shoup cryptosystem has attracted much attention from the research community, mainly due to its efficiency in encryption/decryption, as well as the provable reductions of security against adaptively chosen ciphertext attacks in the standard model. At TCC 2005, Vasco et al. proposed a method for building Cramer-Shoup like cryptosystem over non-abelian groups and raised an open problem for finding a secure instantiation. Based on this work, we present another general framework for constructing Cramer-Shoup like cryptosystems. We firstly propose the concept of index exchangeable family (IEF) and an abstract construction of CramerShoup like encryption scheme over IEF. The concrete instantiations of IEF are then derived from some reasonable hardness assumptions over abelian groups as well as non-abelian groups, respectively. These instantiations ultimately lead to simple yet efficient constructions of Cramer-Shoup like cryptosystems, including new non-abelian analogies that can be potential solutions to Vasco et al.'s open problem. Moreover, we propose a secure outsourcing method for the encryption of the non-abelian analog based on the factorization problem over non-commutative groups. The experiments clearly indicate that the computational cost of our outsourcing scheme can be significantly reduced thanks to the load sharing with cloud datacenter servers.