On Generating Random Variates from an Empirical Distribution

Chen, Hui-Chuan; Asau, Yoshinori

doi:10.1080/05695557408974949

Cited by 68 publications

(25 citation statements)

References 3 publications

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“…One contribution of this work are improved techniques for efficient sampling of Gaussian noise that support parameters required for digital signature schemes such as Bliss and similar constructions. First, we detail how to accelerate the binary search on a cumulative distribution table (CDT) using a shortcut table of intervals (also known as guide table [9,11]) and develop an optimal data structure that saves roughly half of the table space by exploiting the properties of the Kullback-Leibler divergence. Furthermore, we apply a convolution lemma [29] for discrete Gaussians that results in even smaller tables of less than 2.1 KB for Bliss-I parameters.…”

Section: Introductionmentioning

confidence: 99%

Enhanced Lattice-Based Signatures on Reconfigurable Hardware

Pöppelmann

Ducas

Güneysu

2014

Lecture Notes in Computer Science

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Abstract. The recent Bimodal Lattice Signature Scheme (Bliss) showed that lattice-based constructions have evolved to practical alternatives to RSA or ECC. Besides reasonably small signatures with 5600 bits for a 128-bit level of security, Bliss enables extremely fast signing and signature verification in software. However, due to the complex sampling of Gaussian noise with high precision, it is not clear whether this scheme can be mapped efficiently to embedded devices. Even though the authors of Bliss also proposed a new sampling algorithm using Bernoulli variables this approach is more complex than previous methods using large precomputed tables. The clear disadvantage of using large tables for high performance is that they cannot be used on constrained computing environments, such as FPGAs, with limited memory. In this work we thus present techniques for an efficient Cumulative Distribution Table (CDT) based Gaussian sampler on reconfigurable hardware involving Peikert's convolution lemma and the Kullback-Leibler divergence. Based on our enhanced sampler design, we provide a first Bliss architecture for Xilinx Spartan-6 FPGAs that integrates fast FFT/NTT-based polynomial multiplication, sparse multiplication, and a Keccak hash function. Additionally, we compare the CDT with the Bernoulli approach and show that for the particular Bliss-I parameter set the improved CDT approach is faster with lower area consumption. Our core uses 2,431 slices, 7.5 BRAMs, and 6 DSPs and performs a signing operation in 126 µs on average. Verification takes even less with 70 µs.

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Section: Introductionmentioning

confidence: 99%

Enhanced Lattice-Based Signatures on Reconfigurable Hardware

Pöppelmann

Ducas

Güneysu

2014

Lecture Notes in Computer Science

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“…Moro [19] contains an implementation of an inverse transformation algorithm. Also, the empirical distribution method of Chen and Asau [5] can be applied to standard normal distribution. Several other methods are also available for generating normal variates.…”

Section: A N(µ σmentioning

confidence: 99%

Rectangles algorithm for generating normal variates

Zhang

Leemis

2011

Naval Research Logistics

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Abstract:We propose an algorithm for generating normal random variates that is based on the acceptance-rejection method and uses a piecewise majorizing function. The piecewise function has 2048 equal-area pieces, 2046 of which are constant, and the two extreme pieces are curves that majorize the tails. The proposed algorithm has not only good performance from correlation induction perspective, but also works well from a speed perspective. It is faster than the inversion method by Odeh and Evans and most other methods.

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“…Another class of techniques use indexing or buckets to speed up the search (Chen and Asau, 1974;Bratley et al, 1987;Devroye, 1986). For example, one can partition the interval (0, 1) into c subintervals of equal sizes and use (pretabulated) initial values of (L, R) that depend on the subinterval in which U falls.…”

Section: Inversionmentioning

confidence: 99%