Secure Computation with Non-Equivalent Penalties in Constant Rounds

It is known that Bitcoin enables to achieve fairness in secure computation by imposing a monetary penalty on adversarial parties. This functionality is called secure computation with penalties . Bentov and Kumaresan (Crypto 2014) showed that it could be realized with O ( n ) rounds and O ( n ) broadcasts for any function, where n is the number of parties. Kumaresan and Bentov (CCS 2014) posed an open question: “Is it possible to design secure computation with penalties that needs only O (1) rounds and O ( n ) broadcasts?” In this work, we introduce secure computation with non-equivalent penalties , and design a protocol achieving this functionality with O (1) rounds and O ( n ) broadcasts only. The new functionality is the same as secure computation with penalties except that every honest party receives more than a predetermined amount of compensation while the previous one requires that every honest party receives the same amount of compensation. In particular, both are the same if all parties behave honestly. Thus, our result gives a partial answer to the open problem with a slight and natural modification of functionality.