Predictive Models for Min-entropy Estimation

Kelsey, John; McKay, Kerry A.; Turan, Meltem Sönmez

doi:10.1007/978-3-662-48324-4_19

Cited by 27 publications

(45 citation statements)

References 10 publications

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“…The calculations for the local entropy estimate come from the probability theory of runs and recurrent events [Fel50]. For more information about min-entropy estimation using predictors, see [Kel15].…”

Section: G2 Predictorsmentioning

confidence: 99%

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Recommendation for the entropy sources used for random bit generation

Turan¹,

Barker²,

Kelsey³

et al. 2018

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AuthorityThis publication has been developed by NIST in accordance with its statutory responsibilities under the Federal Information Security Modernization Act (FISMA) of 2014, 44 U.S.C. § 3551 et seq., Public Law (P.L.) 113-283. NIST is responsible for developing information security standards and guidelines, including minimum requirements for federal information systems, but such standards and guidelines shall not apply to national security systems without the express approval of appropriate federal officials exercising policy authority over such systems. This guideline is consistent with the requirements of the Office of Management and Budget (OMB) Circular A-130.Nothing in this publication should be taken to contradict the standards and guidelines made mandatory and binding on federal agencies by the Secretary of Commerce under statutory authority. Nor should these guidelines be interpreted as altering or superseding the existing authorities of the Secretary of Commerce, Director of the OMB, or any other federal official. This publication may be used by nongovernmental organizations on a voluntary basis and is not subject to copyright in the United States. Attribution would, however, be appreciated by NIST. Any mention of commercial products or reference to commercial organizations is for information only; it does not imply recommendation or endorsement by the United States Government, nor does it imply that the products mentioned are necessarily the best available for the purpose.There may be references in this publication to other publications currently under development by NIST in accordance with its assigned statutory responsibilities. The information in this publication, including concepts and methodologies, may be used by Federal agencies even before the completion of such companion publications. Thus, until each publication is completed, current requirements, guidelines, and procedures, where they exist, remain operative. For planning and transition purposes, Federal agencies may wish to closely follow the development of these new publications by NIST.Organizations are encouraged to review all draft publications during public comment periods and provide feedback to NIST. Many NIST cybersecurity publications, other than the ones noted above, are available at https://csrc.nist.gov/publications. Comments on this publication may be submitted to:National ii This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.800-90B Reports on Computer Systems TechnologyThe Information Technology Laboratory (ITL) at the National Institute of Standards and Technology (NIST) promotes the U.S. economy and public welfare by providing technical leadership for the Nation's measurement and standards infrastructure. ITL develops tests, test methods, reference data, proof of concept implementations, and technical analyses to advance the development and productive use of information technology. ITL's responsibilities include the development of management, administrative, technical, and physical standar...

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Section: G2 Predictorsmentioning

confidence: 99%

“…The first approach is based on entropic statistics, first described for IID data in [HD12], and later applied to non-IID data [HD12]. The second approach is based on predictors, first described in [Kel15].…”

Section: Acronymsmentioning

confidence: 99%

Recommendation for the entropy sources used for random bit generation

Turan¹,

Barker²,

Kelsey³

et al. 2018

Self Cite

227

280

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“…assumption for entropy estimation is dictated by our ignorance about the type of graph to embed and the effect of the embedding function. Recent advances in cryptography [26], where estimating the correct amount of uncertainty is critical, point towards learning techniques that exploit the knowledge available about the random sources (the graphs and the embedding functions). In section 5.5, where we validate the commute time embedding as the most successful embedding function for graph matching/similarity purposes, we will analyze the impact of this choice in the entropy estimator.…”

Section: Motivation and Previous Workmentioning

confidence: 99%

“…Using Lagrange multipliers (one for each constraint), the problem is equivalent to maximizing (26) where the second (entropic) term relies both on an x log(x) barrier function and on β [41]. The third term contains the N (N − 1)/2 − N Lagrange multipliers α ij (one multiplier per constraint).…”

Section: The Optimality Of the Ct Embeddingmentioning

confidence: 99%

“…The moderate power law behavior of Delaunay triangulations in combination with the introduction of large distances between clusters in the CT motivates Θ ij − CT (i, j) < 0 in many cases. The deterministic annealing (DA) algorithm progresses by maximizing (26), which is dominated by the second term 1 β ij:j>i A ij (log A ij −1) for low values of β. However, the elements of the adjacency matrix A ij depend on the Lagrange multipliers α ij (see (27)), which in turn depend on Θ ij − ||x i − x j || 2 = Θ ij − CT (i, j) (28).…”

Section: Deterministic Annealing Algorithmmentioning

confidence: 99%

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Graph Similarity through Entropic Manifold Alignment

Escolano¹,

Hancock²,

Lozano³

2017

SIAM J. Imaging Sci.

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Abstract. In this paper we decouple the problem of measuring graph similarity into two sequential steps.The first step is the linearization of the quadratic assignment problem (QAP) in a low-dimensional space, given by the embedding trick. The second step is the evaluation of an information-theoretic distributional measure, which relies on deformable manifold alignment. The proposed measure is a normalized conditional entropy, which induces a positive definite kernel when symmetrized. We use bypass entropy estimation methods to compute an approximation of the normalized conditional entropy. Our approach, which is purely topological (i.e., it does not rely on node or edge attributes although it can potentially accommodate them as additional sources of information) is competitive with state-of-the-art graph matching algorithms as sources of correspondence-based graph similarity, but its complexity is linear instead of cubic (although the complexity of the similarity measure is quadratic). We also determine that the best embedding strategy for graph similarity is provided by commute time embedding, and we conjecture that this is related to its inversibility property, since the inverse of the embeddings obtained using our method can be used as a generative sampler of graph structure.

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