Proceedings of the 19th international conference on World wide web
Space-efficient local computation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Sparser Johnson-Lindenstrauss transforms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
An energy complexity model for algorithms
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
On the power of correlated randomness in secure computation
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Sparser Johnson-Lindenstrauss Transforms
Journal of the ACM (JACM)
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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 $O(kn+\log \frac{1}{\delta})$.