Pseudorandom Generators for Low Sensitivity Functions
نویسندگان
چکیده
A Boolean function is said to have maximal sensitivity s if s is the largest number of Hamming neighbors of a point which differ from it in function value. We construct a pseudorandom generator with seed-length 2O( √ s) · log(n) that fools Boolean functions on n variables with maximal sensitivity at most s. Prior to our work, the best pseudorandom generators for this class of functions required seed-length 2O(s) · log(n).
منابع مشابه
Correlation bounds for polynomials over {0, 1}1
This article is a unified treatment of the state-of-the-art on the fundamental challenge of exhibiting explicit functions that have small correlation with low-degree polynomials over {0, 1}. It discusses long-standing results and recent developments, related proof techniques, and connections with pseudorandom generators. It also suggests several research directions.
متن کاملMonotone 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.
متن کاملPrivate Key Encryption Instructor : Rafael Pass Scribe : Ashwin Machanavajjhala
Till this point in the course we have learnt how to define secrecy and how to construct tools like one way functions, pseudorandom generators and pseudorandom functions. We will now use the concepts we learnt to construct a secure encryption scheme. In this class we propose a few intuitive definitions for the security of an encryption scheme, show their equivalence and then show a simple constr...
متن کاملExponential sums of nonlinear congruential pseudorandom number generators with Rédei functions
The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. We give new bounds of exponential sums with sequences of iterations of Rédei functions over prime finite fields, which are much stronger than bounds known for general nonlinear congruential pseudorandom number generators. © 2007 Elsevier Inc. All rights ...
متن کاملOn the Existence of Pseudorandom Generators
Pseudorandom generators [BM, Y] are efficient deterministic programs that expand a randomly selected k-bit seed into a much longer pseudorandom bit sequence which is indistinguishable in polynomial-time from a sequence of unbiased coin tosses. Thus, pseudorandom sequences can replace truly random sequences in all practical (i.e. polynomial-time) applications. Pseudorandom generators are known t...
متن کامل