Heuristics: intelligent search strategies for computer problem solving
Heuristics: intelligent search strategies for computer problem solving
One-way functions and circuit complexity
Proc. of the conference on Structure in complexity theory
Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Functions with bounded symmetric communication complexity and circuits with mod m gates
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
One-way functions are necessary and sufficient for secure signatures
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Finding small simple cycle separators for 2-connected planar graphs.
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
A complexity theory for VLSI
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Parallel tree contraction and its application
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Efficiently inverting bijections given by straight line programs
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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In this paper, we study the relation between the multi-party communication complexity over various communication topologies and the complexity of inverting functions and/or permutations. In particular, we show that if a function has a ring-protocol or a tree-protocol of communication complexity bounded by H, then there is a circuit of size O(2Hn) which computes an inverse of the function. Consequently, we have proved, although inverting NC0 Boolean circuits is NP-complete, planar NC1 Boolean circuits can be inverted in NC, and hence in polynomial time. In general, NCk planar boolean circuits can be inverted in O(nlog(k-1)n) time. Also from the ring-protocol results, we derive an 驴(n log n) lower bound on the VLSI area to layout any one-way functions. Our results on inverting boolean circuits can be extended to invert algebraic circuits over finite rings.One significant aspect of our result is that it enables us to compare the communication power of two topologies. We have proved that on some topologies, no one-way function nor its inverse can be computed with bounded communication complexity.