Fair Distributed Oblivious Polynomial Evaluation via Bitcoin Deposits: Compute-as-a-Service

Distributed oblivious polynomial evaluation (DOPE) is a special case of two-party computation where the sender party \(P_1\) holds a polynomial f(x) of degree k and the receiver party \(P_2\) has a value \(\alpha \) . They wish to perform a secure computation with the help of n designated cloud servers such that \(P_2\) obtains the value \(f(\alpha )\) while the privacy of their inputs is maintained. We present the first fair DOPE scheme using Bitcoin deposit transactions in the presence of n cloud servers where n is independent of the polynomial degree k. The fairness property ensures that an honest server gains the reward for conducting a computation service while a corrupt server has to pay some penalty amount to an honest party. Our protocol consists of two separate phases: setup and computation. The cloud servers are involved with \(P_1\) in the setup phase while \(P_2\) communicates with the servers in the computation phase which means that the actual computation can be implemented at any time after the setup phase. Any corrupt party/server can be detected using the non-interactive Pedersen’s commitment scheme. Our protocol preserves the security against an active adversary corrupting a coalition of \(P_1\) and at most t cloud servers in the setup phase and a coalition of up to t servers in the computation phase in the presence of honest majority of the servers. The communication complexity is bounded to O(kt) which is the same as that in the previous DOPE studies while the fairness feature is also achieved in our scheme.