Generating Random Permutations by Coin Tossing

Bacher, Axel; Bodini, Olivier; Hwang, Hsien‐Kuei; Tsai, Tsung-Hsi

doi:10.1145/3009909

Cited by 19 publications

(5 citation statements)

References 48 publications

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“…Our results are only relevant in the context where the generation of random integers is fast compared with the latency of a division operation. In the case where the generation of random bits is likely the bottleneck, other approaches would be preferable [3]. Moreover, our approach may not be applicable to specialized processors such as Graphics Processing Units (GPUs) that lack support for the computation of the full multiplication [17].…”

Section: Resultsmentioning

confidence: 99%

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Fast Random Integer Generation in an Interval

Lemire

2019

ACM Trans. Model. Comput. Simul.

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In simulations, probabilistic algorithms and statistical tests, we often generate random integers in an interval (e.g., [0, s)). For example, random integers in an interval are essential to the Fisher-Yates random shuffle. Consequently, popular languages like Java, Python, C++, Swift and Go include ranged random integer generation functions as part of their runtime libraries.Pseudo-random values are usually generated in words of a fixed number of bits (e.g., 32 bits, 64 bits) using algorithms such as a linear congruential generator. We need functions to convert such random words to random integers in an interval ([0, s)) without introducing statistical biases. The standard functions in programming languages such as Java involve integer divisions. Unfortunately, division instructions are relatively expensive. We review an unbiased function to generate ranged integers from a source of random words that avoids integer divisions with high probability. To establish the practical usefulness of the approach, we show that this algorithm can multiply the speed of unbiased random shuffling on x64 processors. Our proposed approach has been adopted by the Go language for its implementation of the shuffle function.

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Section: Resultsmentioning

confidence: 99%

“…Moreover, our approach may not be applicable to specialized processors such as Graphics Processing Units (GPUs) that lack support for the computation of the full multiplication [17]. 3…”

Section: Resultsmentioning

confidence: 99%

Fast Random Integer Generation in an Interval

Lemire

2019

ACM Trans. Model. Comput. Simul.

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“…This test previously showed that simply choosing random edges from the complete graph does not suffice, as the CIs generated in this example with random edges do not contain the r value calculated by the Mantel Test [2]. [4] The Lp-norm for p ≥ 1 of a vector ⃗ x is a commonly used measure of "distance" in machine learning for clustering, and is defined by To try and address this, we tried implementing step (2) of random-partition() with a parallel shuffling algorithm instead: MergeShuffle [16], which was chosen because of the availability of an implementation that uses OpenMP. The authors of MergeShuffle suggest it is the current fastest parallel shuffling algorithm.…”

Section: Data Set 1: Comparison Of Distance Normsmentioning

confidence: 99%

“…We implemented DC-RST in C++ along with the OpenMP parallel library. The pseudocode is shown below in Step (2) of random-partition() involves shuffling an array of size n-the best known serial algorithm for this is Fisher-Yates, which runs in O(n) time [16].…”

Section: Performance Analysis Implementation Detailsmentioning

confidence: 99%

DC-RST: A Parallel Algorithm for Random Spanning Trees in Network Analytics

Henke

Mehta

2023

Complex Networks and Their Applications XI

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The Mantel Test, discovered in the 1960s, determines whether two distance metrics on a graph are related. We describe DC-RST, an algorithm to accelerate a key step of a network science statistical computation associated with DimeCost, an approach that is faster the Mantel Test. DC-RST is a parallel, divide-and-conquer algorithm to compute a random spanning tree of a complete graph on n vertices. Relative to an implementation of Wilson's sequential random-walk algorithm, on a system with 48 cores, DC-RST was up to 4X faster when first creating random partitions and up to 20X faster without this sub-step. DC-RST is shown to be a suitable replacement for Wilson's sequential algorithm through a combination of theoretical and statistical results.

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“…(3) The pseudo-random bits generated in (1) are used to generate a 16-bit random permutation using the random permutation generation algorithm [25], denoted as , as the S-layer in the lookup table.…”

Section: Spn-as Algorithm Lookup Table Constructionmentioning

confidence: 99%

SPN-AS: A new white-box cryptographic algorithm based on AS iteration structure

Yang

Zhai

Dong

2023

Preprint

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The attacker in white-box model has full access to software implementation of a cryptographic algorithm and full control over its execution environment. In order to solve the issues of high storage cost and inadequate security about most current white-box cryptographic schemes, SPN-AS, a novel white-box block cipher based on AS iterative structure is proposed. This scheme utilizes the AS iterative structure to construct a lookup table with a five-layer ASASA structure, and the maximum distance separable matrix is used as a linear layer to achieve complete diffusion in a small number of rounds. Attackers can be prevented from recovering the key under black-box model. The length of nonlinear layer S and affine layer A in lookup table is 16 bits, which effectively avoids decomposition attack against the ASASA structure and makes the algorithm possess anti-key extraction security under the white-box model, while SPN-AS possesses weak white-box (32KB, 112)-space hardness to satisfy anti-code lifting security. SPN-AS has provable security and better storage cost than existing schemes, with the same anti-key extraction security and anti-code lifting security, only 128KB of memory space is required in SPN-AS, which is only 14% of SPACE-16 algorithm and 33% of Yoroi-16 algorithm.

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Generating Random Permutations by Coin Tossing

Cited by 19 publications

References 48 publications

Fast Random Integer Generation in an Interval

Fast Random Integer Generation in an Interval

DC-RST: A Parallel Algorithm for Random Spanning Trees in Network Analytics

SPN-AS: A new white-box cryptographic algorithm based on AS iteration structure

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