Pseudorandomness for network algorithms

We define pseudorandom generators for Yao’s two-party communication complexity model and exhibit a simple construction, based on expanders, for it. We then use a recursive composition of such generators to obtain pseudorandom generators that fool distributed network algorithms. While the construction and the proofs are simple, we demonstrate the generality of such generators by giving several applications.

[1]  Hugo Krawczyk,et al.  On the Existence of Pseudorandom Generators , 1993, SIAM J. Comput..

[2]  Noam Nisan,et al.  Multiparty protocols and logspace-hard pseudorandom sequences , 1989, STOC '89.

[3]  Leonid A. Levin,et al.  Pseudo-random generation from one-way functions , 1989, STOC '89.

[4]  Andrew Chi-Chih Yao,et al.  Some complexity questions related to distributive computing(Preliminary Report) , 1979, STOC.

[5]  Ingo Wegener,et al.  The complexity of Boolean functions , 1987 .

[6]  B. M. Fulk MATH , 1992 .

[7]  R. Tarjan,et al.  A Separator Theorem for Planar Graphs , 1977 .

[8]  Noam Nisan,et al.  More deterministic simulation in logspace , 1993, STOC.

[9]  Manuel Blum,et al.  How to generate cryptographically strong sequences of pseudo random bits , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[10]  Avi Wigderson,et al.  Deterministic approximate counting of depth-2 circuits , 1993, [1993] The 2nd Israel Symposium on Theory and Computing Systems.

[11]  Bruce A. Reed,et al.  Finding approximate separators and computing tree width quickly , 1992, STOC '92.

[12]  N. Nisan Pseudo-random sequences for space bounded computation , 1992 .

[13]  Noga Alon,et al.  Explicit construction of linear sized tolerant networks , 1988, Discret. Math..

[14]  Andrew Chi-Chih Yao,et al.  Theory and application of trapdoor functions , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[15]  Noam Nisan,et al.  Hardness vs Randomness , 1994, J. Comput. Syst. Sci..

[16]  Johan Håstad,et al.  Pseudo-random generators under uniform assumptions , 1990, STOC '90.

[17]  Avi Wigderson,et al.  Deterministic simulation of probabilistic constant depth circuits , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[18]  Noam Nisan,et al.  Pseudorandom bits for constant depth circuits , 1991, Comb..

[19]  Alexander Lubotzky,et al.  Explicit expanders and the Ramanujan conjectures , 1986, STOC '86.

[20]  Noam Nisan,et al.  BPP has subexponential time simulations unlessEXPTIME has publishable proofs , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[21]  Noam Nisan,et al.  Hardness vs. randomness , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[22]  Robin Thomas,et al.  A separator theorem for graphs with an excluded minor and its applications , 1990, STOC '90.