Efficient and Secure Batch Exponentiations Outsourcing in Cloud Computing

Cloud computing is an emerging computing paradigm in which IT resources and capacities are provided as services over the Internet. Promising as it is, this paradigm also brings forth new challenges for security when users want to securely outsource the computation of cryptographic operations to the untrusted cloud servers. As we know, modular exponentiation is one of basic operations among most of current cryptosystems. In this paper, we present two generic secure outsourcing schemes enabling users to securely outsource the computations of exponentiations to cloud servers. The first one is a secure outsourcing scheme for fixed base-variable exponent exponentiation, while the second is for fixed exponent-variable base exponentiation. With our techniques, a batch of exponentiations (eg. t exponentiations) can be efficiently computed by the user with only (n+t) multiplications, where n is the number of bits of the exponent. Furthermore, there is not any pre-computation on the user side. The schemes are proved to be secure under the Hidden Subset Sum Problem.