Abstract
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(2H n) which computes an inverse of the function. Consequently, we have proved, although inverting NC 0 Boolean circuits is N P-complete, planar N C 1 Boolean circuits can be inverted in N C, and hence in polynomial time. In general, NC k planar boolean circuits can be inverted in O(n log(k−1) n) time. Also from the ring-protocol results, we derive an Ω(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.
This work was supported in part by National Science Foundation grant DCR-8713489. Part of this work was done while the author was at School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213.
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© 1992 Springer-Verlag Berlin Heidelberg
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Teng, SH. (1992). Functional Inversion and Communication Complexity. In: Feigenbaum, J. (eds) Advances in Cryptology — CRYPTO ’91. CRYPTO 1991. Lecture Notes in Computer Science, vol 576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46766-1_18
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DOI: https://doi.org/10.1007/3-540-46766-1_18
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