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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Maurer, U., Pietrzak, K. (2004). Composition of Random Systems: When Two Weak Make One Strong. In: Naor, M. (eds) Theory of Cryptography. TCC 2004. Lecture Notes in Computer Science, vol 2951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24638-1_23
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DOI: https://doi.org/10.1007/978-3-540-24638-1_23
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