International Association
for Cryptologic Research

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 {\\em 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 {\\em arbitrary} commutative group:

\\begin{enumerate}

\\item Group inverses, with security and privacy holding against any computationally unrestricted malicious server.

\\item Group exponentiation, with security and privacy holding against any computationally unrestricted ``partially honest\" server.

\\item Group exponentiation, with security and privacy holding against any polynomial-time malicious server, under a pseudorandom generation assumption, and security holding with constant probability.

\\end{enumerate}