This paper demonstrates that Shamir's scheme is not secure against certain forms of cheating, and a small modification to his scheme retains the security and efficiency of the original and preserves the property that its security does not depend on any unproven assumptions such as the intractability of computing number-theoretic functions.Expand

New upper bounds on the complexity of the certified write-all problem with respect to an adaptive adversary are proved and it is shown that for any $\epsilon > 0$, there exists an $O(p^{1+\ep silon})$ work algorithm for the p-processor $p-memory cell write- all.Expand

This paper presents an optimally fast and highly resilient shared-memory randomized consensus algorithm that runs in only O(log n) expected time if @or less failures occur, and takes at most O(*) expected tim~ for any j.Expand

It is shown that any "random self-reducible" problem has a zero knowledge interactive proof of this sort, and new zeroknowledge 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*.Expand

This paper gives a wait-free implementation of an efficient algorithm for union-find and shows that the worst case performance of the algorithm can be improved by simulating a synchronized algorithm, or bysimulating a larger machine if the data structure requests support sufficient parallelism.Expand

It is demonstrated that Shamir's scheme is not secure against cheating, and a small modification to his scheme retains the security and efficiency of the original, and preserves the property that its security does not depend on any unproven assumptions such as the intractability of computing number-theoretic functions.Expand

An overview of reductions among the problems of integer factorization and the discrete logarithm problem gives an overview of new reductions from squarefreeness to Euler's function φ ( n ), and a probabilistic polynomial time reduction from order modulo a prime power.Expand