Outsourcing computation enables a weak client to expand its computational power as the need arises. A basic requirement of outsourcing computation is the guarantee that the computation result is correct. Cryptographic solutions that provide verifiability for the computation result when the computation is outsourced to a single server, are complex and fragile. We consider the intuitive approach of verifiable computation, called verifiable computation by replication, when the computation is replicated on multiple servers, and a referee decides the result of the final computation using the outputs of all servers. We consider the case when a smart contact is used as the referee. We propose a security model in the Universal Composability (UC) framework of Canetti, and design a 2-server and an n-server protocol with proved security in our model. Our protocols build on the Refereed Delegation of Computation (RDoC) framework of Canetti, Riva, and Rothblum, underline the challenges of using a smart contract as a referee, and address those challenges in the designed protocols. We give the efficiency analysis of the protocols, provide a proof of concept implementation for our protocols using Ethereum smart contact, and give concrete cost values for an example computation.

Abstract Fair exchange protocols are among the most important cryptographic primitives in electronic commerce. A basic fair exchange protocol requires that two parties who want to exchange their digital items either receive what they have been promised, or lose nothing. Privacy of fair exchange requires that no one else (other than the two parties) learns anything about the items. Fairness and privacy have been considered as two distinct properties of an exchange protocol. In this paper, we show that subtle ways of leaking the exchange item to the third parties affect fairness in fair exchange protocols when the item is confidential. Our focus is on Fair-Swap, a recently proposed fair exchange protocol that uses a smart contract for dispute resolution, has proven security in UC (Universal Composability) framework, and provides privacy when both parties are honest. We demonstrate, however, that FairSwap’s dispute resolution protocol leaks information to the public and this leakage provides opportunities for the dishonest parties to influence the protocol’s fairness guarantee. We then propose an efficient privacy-enhanced version of Fair-Swap, prove its security and give an implementation and performance evaluation of our proposed system. Our privacy enhancement uses circuit randomization, and we prove its security and privacy in an extension of universal composability model for non-monolithic adversaries that would be of independent interest.