On a Set of Almost Deterministic $k$-Independent Random Variables

Joffe, A.

doi:10.1214/aop/1176996762

Cited by 103 publications

(48 citation statements)

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“…Efficient constructions of k-wise independent functions have been known for some time [Jof74,KM94], and they have been used extensively in the derandomization literature [Lub85,ABI86,KM93]. One common approach to construct a k-wise independent function f from X to Y is to assume that N = |Y| is a prime power and interpret Y as the field F N .…”

Section: Simulating Random Oraclesmentioning

confidence: 99%

Secure Identity-Based Encryption in the Quantum Random Oracle Model

Zhandry

2012

Lecture Notes in Computer Science

137

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We give the first proof of security for an identity-based encryption scheme in the quantum random oracle model. This is the first proof of security for any scheme in this model that requires no additional assumptions. Our techniques are quite general and we use them to obtain security proofs for two random oracle hierarchical identity-based encryption schemes and a random oracle signature scheme, all of which have previously resisted quantum security proofs, even using additional assumptions. We also explain how to remove the extra assumptions from prior quantum random oracle model proofs. We accomplish these results by developing new tools for arguing that quantum algorithms cannot distinguish between two oracle distributions. Using a particular class of oracle distributions, so called semi-constant distributions, we argue that the aforementioned cryptosystems are secure against quantum adversaries.

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Section: Simulating Random Oraclesmentioning

confidence: 99%

Secure Identity-Based Encryption in the Quantum Random Oracle Model

Zhandry

2012

Lecture Notes in Computer Science

137

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“…The use of limited independence in computer science originates with the seminal papers of Carter and Wegman [93,417], which introduced the notions of universal, strongly universal (i.e., k-wise independent), and almost strongly universal (i.e., almost k-wise independent) families of hash functions. The pairwise independent and k-wise independent sample spaces of Constructions 3.18, 3.23, and 3.32 date back to the work of Lancaster [255] and Joffe [222,223] in the probability literature, and were rediscovered several times in the computer science literature. The construction of pairwise independent hash functions from Part 1 of Problem 3.3 is due to Carter and Wegman [93] and Part 2 is implicit in [408,168].…”

Section: Chapter Notes and Referencesmentioning

confidence: 99%

Chapter 8 Notes and References

2011

Feynman-Kac-Type Theorems and Gibbs Measures on Path Space

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“…k-wise independent random variables were first studied in probability theory [23] and then in complexity theory [13,2,28,29] mainly for derandomization purposes. Constructions of almost k-wise independent distributions were studied in [31,3,6,17,10].…”

Section: Other Related Researchmentioning

confidence: 99%

“…Furthermore, k-wise independent distributions can be constructed with exponentially smaller support sizes than fully independent distributions. Because of these useful properties, k-wise independent distributions have many applications in both probability theory and computational complexity theory [23,25,28,31].…”

Section: Introductionmentioning

confidence: 99%

Testing Non-uniform k-Wise Independent Distributions over Product Spaces

Rubinfeld

Xie

2010

Automata, Languages and Programming

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Abstract. A distribution D over Σ1 × · · · × Σn is called (non-uniform) k-wise independent if for any set of k indices {i1, . . . , i k } and for any z1We study the problem of testing (non-uniform) k-wise independent distributions over product spaces. For the uniform case we show an upper bound on the distance between a distribution D from the set of k-wise independent distributions in terms of the sum of Fourier coefficients of D at vectors of weight at most k. Such a bound was previously known only for the binary field. For the non-uniform case, we give a new characterization of distributions being k-wise independent and further show that such a characterization is robust. These greatly generalize the results of Alon et al.[1] on uniform k-wise independence over the binary field to non-uniform k-wise independence over product spaces. Our results yield natural testing algorithms for k-wise independence with time and sample complexity sublinear in terms of the support size when k is a constant. The main technical tools employed include discrete Fourier transforms and the theory of linear systems of congruences.A full version of this paper is available at

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On a Set of Almost Deterministic $k$-Independent Random Variables

Cited by 103 publications

References 0 publications

Secure Identity-Based Encryption in the Quantum Random Oracle Model

Secure Identity-Based Encryption in the Quantum Random Oracle Model

Chapter 8 Notes and References

Testing Non-uniform k-Wise Independent Distributions over Product Spaces

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