In this paper, we prove new upper bounds on the complexity of the certified write-all problem with respect to an adaptive adversary. Our strongest result is that for any $\epsilon > 0$, there exists an $O(p^{1+\epsilon})$ work algorithm for the p-processor p-memory cell write-all. We also give a randomized $O(p^2\log p)$ work algorithm for a p-processor $p^2$-memory cell write-all.

We are interested in designing efficient data structures for a shared memory multiprocessor. In this paper we focus on the Union-Find data structure. We consider a fully asynchronous model of computation where arbitrary delays are possible. Thus we require our solutions to the data structure problem have the wait-free property, meaning that each thread continues to make progress on its operations, independent of the speeds of the other threads. In this model efficiency is best measured in terms of the total number of instructions used to perform a sequence of data structure operations, the work performed by the processors. We give a wait-free implementation of an efficient algorithm for Union-Find. In addition we show that the worst case performance of the algorithm can be improved by simulating a synchronized algorithm, or by simulating a larger machine if the data structure requests support sufficient parallelism. Our solutions apply to a much more general adversary model than has be...

The notion of a zero knowledge interactive proof that one party "knows" some secret information is explored. It is shown that any "random self-reducible" problem has a zero knowledge interactive proof of this sort. The zero knowledge interactive proofs for graph isomorphism, quadratic residuosity, and "knowledge" of discrete logarithms all follow as special cases. Based on these results, new zero knowledge interactive proofs are exhibited for "knowledge" of the factorization of an integer, nonmembership in cyclic subgroups of Zp*, and determining whether an element generates Zp*. None of these proofs relies on any unproven assumptions.