This paper presents an efficient asynchronous protocol to compute RSA inverses with respect to a public RSA modulus N whose factorization is secret and shared among a group of parties. Given two numbers x and e, the protocol computes y such that ye=x (mod N). A synchronous protocol for this task has been presented by Catalano, Gennaro, and Halevi (Eurocrypt 2000), but the standard approach for turning this into an asynchronous protocol would require a Byzantine-agreement sub-protocol. Our protocol adopts their approach, but exploits a feature of the problem in order to avoid the use of a Byzantine agreement primitive. Hence, it leads to efficient asynchronous protocols for threshold signatures and for Byzantine agreement based on the strong RSA assumption, without the use of random oracles.

This book constitutes the refereed proceedings of the 24th International Symposium on Distributed Computing, DISC 2010, held in Cambridge, CT, USA, in September 2010. The 32 revised full papers, selected from 135 submissions, are presented together with 14 brief announcements of ongoing works; all of them were carefully reviewed and selected for inclusion in the book. The papers address all aspects of distributed computing, and were organized in topical sections on, transactions, shared memory services and concurrency, wireless networks, best student paper, consensus and leader election, mobile agents, computing in wireless and mobile networks, modeling issues and adversity, and self-stabilizing and graph algorithms.