Abstract: "This paper investigates one-round secure computation between two distrusting parties: Alice and Bob each have private inputs to a common function, but only Alice, acting as the receiver, is to learn the output; the protocol is limited to one message from Alice to Bob followed by one message from Bob to Alice. A model in which Bob may be computationally unbounded is investigated, which corresponds to information-theoretic security for Alice. It is shown that 1. for honest-but-curious behavior and unbounded Bob, any function computable by a polynomial-size circuit can be computed securely assuming the hardness of the decisional Diffie-Hellman problem; 2. for malicious behavior by both (bounded) parties, any function computable by a polynomial-size circuit can be computed securely, in a public-key framework, assuming the hardness of the decisional Diffie-Hellman problem. The results are applied to secure autonomous mobile agents, which migrate between several distrusting hosts before returning to their originator. A scheme is presented for protecting the agent's secrets such that only the originator learns the output of the computation."