Derandomized constructions of k-wise (almost) independent permutations

Eyal Kaplan, Moni Naor, Omer Reingold

    Research output: Contribution to journalArticlepeer-review


    Constructions of k-wise almost independent permutations have been receiving a growing amount of attention in recent years. However, unlike the case of k-wise independent functions, the size of previously constructed families of such permutations is far from optimal. This paper gives a new method for reducing the size of families given by previous constructions. Our method relies on pseudorandom generators for space-bounded computations. In fact, all we need is a generator, that produces "pseudorandom walks" on undirected graphs with a consistent labelling. One such generator is implied by Reingold's log-space algorithm for undirected connectivity (Reingold/Reingold et al. in Proc. of the 37th/38th Annual Symposium on Theory of Computing, pp. 376-385/457-466, 2005/2006). We obtain families of k-wise almost independent permutations, with an optimal description length, up to a constant factor. More precisely, if the distance from uniform for any k tuple should be at most δ, then the size of the description of a permutation in the family is O(kn+ log 1/δ).

    Original languageEnglish
    Pages (from-to)113-133
    Number of pages21
    Issue number1
    StatePublished - Sep 2009


    • Block ciphers
    • Card shuffling
    • Connectivity
    • Pseudo-randomness
    • Random walk


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