Information Security and Cryptography Research Group

Composition of Random Systems: When Two Weak Make One Strong

Ueli Maurer and Krzysztof Pietrzak

Theory of Cryptography Conference — TCC 2004, Lecture Notes in Computer Science, Springer-Verlag, vol. 2951, pp. 410–427, Feb 2004.

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 $\bf F$, relative to another random system $\bf G$, whose probability of occurring for a given distinguisher $\bf D$ is closely related to the distinguishing advantage $\varepsilon$ of $\bf D$ for $\bf F$ and $\bf G$, namely it is lower and upper bounded by $\varepsilon$ and $\varepsilon(1+\ln \frac{1}{\varepsilon})$, 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).

BibTeX Citation

    author       = {Ueli Maurer and Krzysztof Pietrzak},
    title        = {Composition of Random Systems: When Two Weak Make One Strong},
    editor       = {Moni Naor},
    booktitle    = {Theory of Cryptography Conference --- TCC 2004},
    pages        = {410--427},
    series       = {Lecture Notes in Computer Science},
    volume       = {2951},
    year         = {2004},
    month        = {2},
    publisher    = {Springer-Verlag},

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