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Delayed path coupling and generating random permutations via distributed stochastic processes
, 1999
"... We analyze various stochastic processes for generating permutations almost uniformly at random in distributed and parallel systems. All our protocols are simple, elegant and are based on performing disjoint transpositions executed in parallel. The challenging problem of our concern is to prove that ..."
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Cited by 18 (3 self)
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We analyze various stochastic processes for generating permutations almost uniformly at random in distributed and parallel systems. All our protocols are simple, elegant and are based on performing disjoint transpositions executed in parallel. The challenging problem of our concern is to prove that the output configurations in our processes reach almost uniform probability distribution very rapidly, i.e. in a (low) polylogarithmic time. For the analysis of the aforementioned protocols we develop a novel technique, called delayed path coupling, for proving rapid mixing of Markov chains. Our approach is an extension of the path coupling method of Bubley and Dyer. We apply delayed path coupling to three stochastic processes for generating random permutations. For one
How to Encipher Messages on a Small Domain Deterministic Encryption and the Thorp Shuffle
 APPEARS IN ADVANCES IN CRYPTOLOGY – CRYPTO 2009
, 2009
"... We analyze the security of the Thorp shuffle, or, equivalently, a maximally unbalanced Feistel network. Roughly said, the Thorp shuffle on N cards mixes any N 1−1/r of them in O(r lg N) steps. Correspondingly, making O(r) passes of maximally unbalanced Feistel over an nbit string ensures CCAsecuri ..."
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Cited by 8 (4 self)
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We analyze the security of the Thorp shuffle, or, equivalently, a maximally unbalanced Feistel network. Roughly said, the Thorp shuffle on N cards mixes any N 1−1/r of them in O(r lg N) steps. Correspondingly, making O(r) passes of maximally unbalanced Feistel over an nbit string ensures CCAsecurity to 2 n(1−1/r) queries. Our results, which employ Markovchain techniques, enable the construction of a practical and provablysecure blockcipherbased scheme for deterministically enciphering credit card numbers and the like using a conventional blockcipher.
Efficient Sampling of Random Permutations
 IN &QUOT;J. ON DISCRETE ALGORITHMS&QUOT;, ACCEPTED
, 2005
"... We show how to uniformly distribute data at random (not to be confounded with permutation routing) in two settings that are able to deal with massive data: coarse grained parallelism and external memory. In contrast to previously known work for parallel setups, our method is able to fulfill the thre ..."
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Cited by 5 (0 self)
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We show how to uniformly distribute data at random (not to be confounded with permutation routing) in two settings that are able to deal with massive data: coarse grained parallelism and external memory. In contrast to previously known work for parallel setups, our method is able to fulfill the three criteria of uniformity, workoptimality and balance among the processors simultaneously. To guarantee the uniformity we investigate the matrix of communication requests between the processors. We show that its distribution is a generalization of the multivariate hypergeometric distribution and we give algorithms to sample it efficiently in the two settings.
A Synopsis of FormatPreserving Encryption
 UNPUBLISHED MANUSCRIPT
, 2010
"... Formatpreserving encryption (FPE) encrypts a plaintext of some specified format into a ciphertext of the same format—for example, encrypting a socialsecurity number into a socialsecurity number. In this survey we describe FPE and review known techniques for achieving it. These include FFX, a rece ..."
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Cited by 3 (0 self)
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Formatpreserving encryption (FPE) encrypts a plaintext of some specified format into a ciphertext of the same format—for example, encrypting a socialsecurity number into a socialsecurity number. In this survey we describe FPE and review known techniques for achieving it. These include FFX, a recent proposal made to NIST.
Switching Networks for Generating Random Permutations
 Advances in Switching Networks
, 2001
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Sequential Random Permutation, List Contraction and Tree Contraction are Highly Parallel
"... We show that simple sequential randomized iterative algorithms for random permutation, list contraction, and tree contraction are highly parallel. In particular, if iterations of the algorithms are run as soon as all of their dependencies have been resolved, the resulting computations have logarit ..."
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Cited by 1 (1 self)
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We show that simple sequential randomized iterative algorithms for random permutation, list contraction, and tree contraction are highly parallel. In particular, if iterations of the algorithms are run as soon as all of their dependencies have been resolved, the resulting computations have logarithmic depth (parallel time) with high probability. Our proofs make an interesting connection between the dependence structure of two of the problems and random binary trees. Building upon this analysis, we describe linearwork, polylogarithmicdepth algorithms for the three problems. Although asymptotically no better than the many prior parallel algorithms for the given problems, their advantages include very simple and fast implementations, and returning the same result as the sequential algorithm. Experiments on a 40core machine show reasonably good performance relative to the sequential algorithms. 1
271 Delayed Path Coupling and Generating Random Permutations Stochastic Processes * via Distributed
"... We analyze various stochastic processes for generating permutations almost uniformlv at random in distributed and parallel systems. All our protocols are simple, elegant and &e based on performing disjoint transpositions executed in narallel. The challentine: problem of our concern is to Drove t ..."
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We analyze various stochastic processes for generating permutations almost uniformlv at random in distributed and parallel systems. All our protocols are simple, elegant and &e based on performing disjoint transpositions executed in narallel. The challentine: problem of our concern is to Drove that the output confi&%ions in our processes reach Amost uniform probability distribution very rapidly, i.e. in a (low) polylogarithmic time. For the analysis of the aforementioned protocols we develop a novel technique, called delayed path coupling, for proving rapid mixing of Markov chains. Our approach is an extension of the path coupling method of Bubley and Dyer. We apply delayed path coupling to three stochastic processes for generating random permutations. For one
1.1. Problem of Random Permuting
, 1999
"... ABSTRACT: We consider the problem of generating permutations almost uniformly at random in distributed and parallel systems. We propose a simple distributed scheme for permuting at random, which we call distributed mixing, and provide its precise stochastic analysis. Our main result is that distribu ..."
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ABSTRACT: We consider the problem of generating permutations almost uniformly at random in distributed and parallel systems. We propose a simple distributed scheme for permuting at random, which we call distributed mixing, and provide its precise stochastic analysis. Our main result is that distributed mixing needs ��log n � simple pointtopoint communication rounds to generate a permutation almost uniformly at random. We further apply distributed mixing to design very fast parallel algorithms for OCPC and QRQW parallel computers (with runtimes ��log log n � and � � √ log n� � respectively). Our analysis of distributed mixing is based on the analysis of the mixing time of the Markov chain governing the process. The main technical tool developed in the paper is a novel method of analyzing convergence of Markov chains. Our method, called delayed path coupling, is a refinement of the classical coupling technique and the path coupling technique of Bubley and Dyer, and its main, novel feature is the use of possible nonMarkovian coupling. © 2000 John Wiley & Sons, Inc.
Is Your Permutation Algorithm Unbiased for n ̸ = 2 m?
"... Abstract. Many papers on parallel random permutation algorithms assume the input size n to be a power of two and imply that these algorithms can be easily generalized to arbitrary n, e.g., by padding the input array to a power of two. We show that this simplifying assumption is not necessarily corre ..."
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Abstract. Many papers on parallel random permutation algorithms assume the input size n to be a power of two and imply that these algorithms can be easily generalized to arbitrary n, e.g., by padding the input array to a power of two. We show that this simplifying assumption is not necessarily correct since it may result in a bias (i.e., not all possible permutations are generated with equal likelihood). Many of these algorithms are, however, consistent, i.e., iterating them ultimately converges against an unbiased permutation. We prove this convergence along with proving exponential convergence speed. Furthermore, we present an analysis of iterating applied to a butterfly permutation network, which works inplace and is wellsuited for implementation on manycore systems such as GPUs. We also show a method that improves the convergence speed even further and yields a practical implementation of the permutation network on current GPUs.
Sharedmemory parallelism can be simple, . . .
, 2015
"... Parallelism is the key to achieving high performance in computing. However, writing efficient and scalable parallel programs is notoriously difficult, and often requires significant expertise. To address this challenge, it is crucial to provide programmers with highlevel tools to enable them to de ..."
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Parallelism is the key to achieving high performance in computing. However, writing efficient and scalable parallel programs is notoriously difficult, and often requires significant expertise. To address this challenge, it is crucial to provide programmers with highlevel tools to enable them to develop solutions efficiently, and at the same time emphasize the theoretical and practical aspects of algorithm design to allow the solutions developed to run efficiently under all possible settings. This thesis addresses this challenge using a threepronged approach consisting of the design of sharedmemory programming techniques, frameworks, and algorithms for important problems in computing. The thesis provides evidence that with appropriate programming techniques, frameworks, and algorithms, sharedmemory programs can be simple, fast, and scalable, both in theory and in practice. The results developed in this thesis serve to ease the transition into the multicore era. The first part of this thesis introduces tools and techniques for deterministic