Robust pseudorandom generators

  • Authors:

  • Yuval Ishai;Eyal Kushilevitz;Xin Li;Rafail Ostrovsky;Manoj Prabhakaran;Amit Sahai;David Zuckerman

  • Affiliations:

  • Technion, Israel;Technion, Israel;University of Washington;University of California, Los Angeles;University of Illinois at Urbana-Champaign;University of California, Los Angeles;University of Texas at Austin

  • Venue:
  • ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
  • Year:
  • 2013

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Abstract

Let G:{0,1}n→{0,1}m be a pseudorandom generator. We say that a circuit implementation of G is (k,q)-robust if for every set S of at most k wires anywhere in the circuit, there is a set T of at most q|S| outputs, such that conditioned on the values of S and T the remaining outputs are pseudorandom. We initiate the study of robust PRGs, presenting explicit and non-explicit constructions in which k is close to n, q is constant, and mn. These include unconditional constructions of robust r-wise independent PRGs and small-bias PRGs, as well as conditional constructions of robust cryptographic PRGs. In addition to their general usefulness as a more resilient form of PRGs, our study of robust PRGs is motivated by cryptographic applications in which an adversary has a local view of a large source of secret randomness. We apply robust r-wise independent PRGs towards reducing the randomness complexity of private circuits and protocols for secure multiparty computation, as well as improving the "black-box complexity" of constant-round secure two-party computation.