Monotone Circuits: One-Way Functions versus Pseudorandom Generators

We study the computability of one-way functions and pseudorandom generators by monotone circuits, showing a substantial gap between the two: On one hand, there exist one-way functions that are computable by (uniform) polynomial-size monotone functions, provided (of course) that one-way functions exist at all. On the other hand, no monotone function can be a pseudorandom generator.

[1]  Nathan Linial,et al.  The influence of variables on Boolean functions , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[2]  Yuval Ishai,et al.  Cryptography in NC0 , 2004, SIAM J. Comput..

[3]  János Komlós,et al.  An 0(n log n) sorting network , 1983, STOC.

[4]  Leonid A. Levin,et al.  A Pseudorandom Generator from any One-way Function , 1999, SIAM J. Comput..

[5]  Oded Goldreich,et al.  Computational complexity: a conceptual perspective , 2008, SIGA.

[6]  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).

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

[8]  B. Applebaum.  Cryptography in NC0 , 2014 .

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

[10]  Richard E. Overill,et al.  Foundations of Cryptography: Basic Tools , 2002, J. Log. Comput..

[11]  Michel Talagrand,et al.  How much are increasing sets positively correlated? , 1996, Comb..

[12]  E. Szemerédi,et al.  O(n LOG n) SORTING NETWORK. , 1983 .