Composition of Random Systems: When Two Weak Make One Strong

  • Ueli Maurer
  • Krzysztof Pietrzak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2951)

Abstract

A new technique for proving the adaptive indistinguishability of two systems, each composed of some component systems, is presented, using only the fact that corresponding component systems are non-adaptively indistinguishable. The main tool is the definition of a special monotone condition for a random system F, relative to another random system G, whose probability of occurring for a given distinguisher D is closely related to the distinguishing advantage ε of D for F and G, namely it is lower and upper bounded by ε and \(\epsilon(1 + {\rm ln}\frac{1}{\epsilon})\), respectively.

A concrete instantiation of this result shows that the cascade of two random permutations (with the second one inverted) is indistinguishable from a uniform random permutation by adaptive distinguishers which may query the system from both sides, assuming the components’ security only against non-adaptive one-sided distinguishers.

As applications we provide some results in various fields as almost k-wise independent probability spaces, decorrelation theory and computational indistinguishability (i.e., pseudo-randomness).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ueli Maurer
    • 1
  • Krzysztof Pietrzak
    • 1
  1. 1.Department of Computer ScienceETH Zürich 

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