Efficient and Secure Delegation of Group Exponentiation to a Single Server

We consider the problem of delegating computation of group operations from a computationally weaker client holding an input and a description of a function, to a single computationally stronger server holding a description of the same function. Solutions need to satisfy natural correctness, security, privacy and efficiency requirements. We obtain delegated computation protocols for the following functions, defined for an arbitrary commutative group: 1. Group inverses, with security and privacy holding against any computationally unrestricted malicious server. 2. Group exponentiation, with security and privacy holding against any computationally unrestricted “partially honest” server. 3. Group exponentiation, with security and privacy holding against any polynomial-time malicious server, under a pseudorandom generation assumption, and security holding with constant probability.