Optimistic Asynchronous Multi-party Contract Signing with Reduced Number of Rounds

Optimistic asynchronous multi-party contract signing protocols have received attention in recent years as a compromise between efficient protocols and protocols avoiding a third party as a bottleneck of security. “Optimistic“ roughly means: in case all participants are honest and receive the messages from the other participants as expected, the third party is not involved at all. The best solutions known so far terminate within t + 2 rounds in the optimistic case, for any fixed set of n signatories and allowing up to t < n dishonest signatories. The protocols presented here achieve a major improvement compared to the state of the art: The number of rounds R is reduced from O(t) to O(1) for all n ≤ 2t + 1, and for n < 2t + 1, R grows remarkably slowly compared with numbers of rounds in $$ o(t):If t \approx \frac{k} {{k + 1}}n then R \approx 2k $$ .