Constant-round linear-broadcast secure computation with penalties

It is known that Bitcoin enables achieving fairness in secure computation by imposing monetary penalties on adversarial parties. This functionality called with penalties. Bentov and Kumaresan (2014) [9] introduced the claim-or-refund can be implemented via Bitcoin. They achieved O(n) rounds broadcasts for any function, where n number of After that, [8] showed a constant-round protocol. Unfortunately, this protocol requires O(n2) broadcasts. As far as we know, no achieves O(1) based work accomplishes such efficiency We first show slightly relaxed setting non-equivalent same except every honest party receives more than predetermined amount compensation, while previous one compensation. Namely, our allows compensations parties to non-equivalent. Moreover, present technique remove non-equivalence without sacrificing efficiency. then propose new ideal claim-refund-or-give