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Algorithms for Exponentiation in Finite Fields

Shuhong Gao, Joachim Von zur gathen, Daniel Panario, Victor Shoup
2000 Journal of symbolic computation  
Gauss periods yield (self-dual) normal bases in finite fields, and these normal bases can be used to implement arithmetic efficiently.  ...  ) operations in Fq, and exponentiation of an arbitrary element in F q n with O(n 2 loglog n) operations in Fq.  ...  A fundamental question for applications is how to do arithmetic fast in finite fields, i.e. addition, multiplication, division, and exponentiation.  ... 
doi:10.1006/jsco.1999.0309 fatcat:y7gcanveqjhf7lksudonw27hlq

Finite Higher Spin Transformations from Exponentiation

Samuel Monnier
2014 Communications in Mathematical Physics  
Exponentiable elements generate one-parameter groups of finite higher spin symmetries.  ...  We show that elements of hs(λ) in a dense set are exponentiable, when pictured in certain representations of hs(λ), induced from representations of SL(2,R) in the complementary series.  ...  This research was supported in part by SNF Grant No.200020-149150/1.  ... 
doi:10.1007/s00220-014-2220-9 fatcat:khagqpi7vndwdf5okkh2nzoihe

Polarization fields in nitride nanostructures: theory and practical implications [article]

Fabio Bernardini, Vincenzo Fiorentini
1998 arXiv   pre-print
Huge built-in electric fields are predicted to exist in wurtzite III-V nitrides thin films and multilayers.  ...  We discuss the theoretical background and the intriguing practical implications of polarization fields for nitride nanostructures.  ...  In this Letter we discuss the theoretical basis and practical implications of polarization fields in nitride nanostructures.  ... 
arXiv:cond-mat/9803384v1 fatcat:kapkwss35jaqdc3gprtt4uqadi

Inflation in exponential scalar model and finite-time singularity induced instability [article]

S.D. Odintsov, V.K. Oikonomou
2015 arXiv   pre-print
Therefore, this infinite singularity indicates that the occurrence of the finite-time singularity is responsible for the instability in the scalar field model we study.  ...  In the context of the exponential model we study, when a Type IV singularity is included in the evolution, an instability occurs in the slow-roll parameters, and in particular on the second slow-roll parameter  ...  Acknowledgments The work of S.O. is supported by MINECO (Spain), projects FIS2010-15640 and FIS2013-44881.  ... 
arXiv:1507.05273v1 fatcat:zbwawysxxrcohbncixvdbqaljq

Efficient Exponentiation for a Class of Finite Fields GF(2 n ) Determined by Gauss Periods [chapter]

Soonhak Kwon, Chang Hoon Kim, Chun Pyo Hong
2003 Lecture Notes in Computer Science  
We present a fast and compact hardware architecture of exponentiation in a finite field GF (2 n ) determined by a Gauss period of type (n, k) with k ≥ 2.  ...  propose a fast exponentiation algorithm which is applicable for both software and hardware purposes.  ...  Introduction Arithmetic of finite fields finds various applications in many cryptographic areas these days.  ... 
doi:10.1007/978-3-540-45238-6_19 fatcat:drsd2r5nyzbzxjfse7gevbextm

Exponential-Family Models of Random Graphs: Inference in Finite-, Super-, and Infinite Population Scenarios [article]

Michael Schweinberger, Pavel N. Krivitsky, Carter T. Butts, Jonathan Stewart
2019 arXiv   pre-print
We then review likelihood-based inference in finite-, super-, and infinite-population scenarios. We conclude with consistency results, and an application to human brain networks  ...  Special cases of ERGMs are generalized linear models (GLMs), Bernoulli random graphs, β-models, p_1-models, and models related to Markov random fields in spatial statistics and other areas of statistics  ...  The seminal work of Berk (1972) and Portnoy (1988) and others demonstrates that statistical theory is easier for exponential families than non-exponential families, and statistical theory for dependent  ... 
arXiv:1707.04800v4 fatcat:zl7gpnoafvbsjjoypw2au7swhe

A Linear Exponential Comonad in s-finite Transition Kernels and Probabilistic Coherent Spaces [article]

Masahiro Hamano
2021 arXiv   pre-print
This paper concerns a stochastic construction of probabilistic coherent spaces by employing novel ingredients (i) linear exponential comonads arising properly in the measure-theory (ii) continuous orthogonality  ...  A linear exponential comonad is constructed over a symmetric monoidal category of transition kernels, relaxing Markov kernels of Panangaden's stochastic relations into s-finite kernels.  ...  Contents Preliminaries from Measure Theory This section recalls some basic definitions and a theorem from measure theory, necessary in this paper.  ... 
arXiv:1909.07589v2 fatcat:jt5t4345trdrplc55x53ww35li

Leakage-Resilient Cryptography over Large Finite Fields: Theory and Practice [chapter]

Marcin Andrychowicz, Daniel Masny, Edoardo Persichetti
2015 Lecture Notes in Computer Science  
In this paper, we present a framework to make cryptographic primitives based on large finite fields robust against information leakage with a bounded computational cost.  ...  The approach makes use of the inner product extractor and guarantees security in the presence of leakage in a widely accepted model.  ...  The results show that our implementation is efficient enough such that it can be considered for applications in practice.  ... 
doi:10.1007/978-3-319-28166-7_32 fatcat:oojeegyvhfcdvljcagn37t7uaa

Variable Resolution Search with Quadrotors: Theory and Practice

Stefano Carpin, Derek Burch, Nicola Basilico, Timothy H. Chung, Mathias Kölsch
2013 Journal of Field Robotics  
Lessons learned from these field trials include characterization of altitude-dependent detection performance and we also present a benchmark data set of outdoor aerial imagery for search and detection  ...  Live-fly field experimentation results using a quadrotor unmanned aerial vehicle validate the proposed methodologies and demonstrate an integrated system with autonomous control and embedded object detection  ...  Any opinions, findings, and conclusions or recommendations expressed in these materials are those of the authors and should not be interpreted as representing the official policies, either expressly or  ... 
doi:10.1002/rob.21468 fatcat:e3rrtlbuhreujedn3lte5yfy7q

Computational information geometry: theory and practice [article]

Karim Anaya-Izquierdo and Frank Critchley and Paul Marriott and Paul W. Vos
2012 arXiv   pre-print
A varied set of substantive running examples is used to illustrate theoretical and practical aspects of the discussion. Further developments are briefly indicated.  ...  Finally, it starts to build a computational framework which will act as a proxy for the 'space of all distributions' that can be used, in particular, to investigate model selection and model uncertainty  ...  Introduction The application of geometry to statistical theory and practice has produced a number of different approaches and this paper will involve three of these.  ... 
arXiv:1209.1988v1 fatcat:y47sva2hyvdzbmlgjt7nzaolqu

Theory and practice unveiled

2007 Biotechnology and Bioengineering  
This paper is based on the significance and utility of the time in Engineering practice and its unpredictability.  ...  However when we are thinking about Engineering practices, the significance of time cannot be ignored .There are various concepts in all the streams of Engineering and technology which are based on time  ...  However in Mechanical Engineering, precisely in Design Engineering there are two concepts infinite life and finite life.  ... 
doi:10.1002/bit.21607 fatcat:5vlq272du5g2ljxzq7sckb4pf4

Mean field theory of demand responsive ride pooling systems

Stephan Herminghaus
2019 Transportation Research Part A: Policy and Practice  
The dynamics of demand responsive ride pooling (DRRP) systems is considered in a mean-field framework.  ...  The relevant dimensionless quantities determining the performance and viability of the system are identified.  ...  Acknowledgement The author appreciates very useful comments and remarks from Marc Timme, Debsankha Manik, Nora Molkenthin, Philip Marszal and Nils Beyer.  ... 
doi:10.1016/j.tra.2018.10.028 fatcat:imcbvemzsrexjnuyiegw6yr2dy

Forecasting: theory and practice [article]

Fotios Petropoulos, Daniele Apiletti, Vassilios Assimakopoulos, Mohamed Zied Babai, Devon K. Barrow, Souhaib Ben Taieb, Christoph Bergmeir, Ricardo J. Bessa, Jakub Bijak, John E. Boylan, Jethro Browell, Claudio Carnevale (+68 others)
2022 arXiv   pre-print
This article provides a non-systematic review of the theory and the practice of forecasting.  ...  and practice.  ...  In the 15 years since the excellent review paper by De Gooijer and , the field of forecasting has seen amazing growth in both theory and practice.  ... 
arXiv:2012.03854v4 fatcat:p32c67sy65cfdejq7ndfs3g7dm

Viscosity at RHIC: Theory and Practice [article]

Scott Pratt
2008 arXiv   pre-print
Hydrodynamic behavior and the associated discussions of viscosity at RHIC has inspired a r enaissance in modeling viscous hydrodynamics.  ...  Interactions and correlations that extend over a finite range contribute to both the shear and bulk viscosities [ 4] .  ...  Unlike the viscous coefficients, σ 2 a and σ 2 b are equal-time correlations and can be calculated from lattice gauge theory without analytic continuation.  ... 
arXiv:0809.0089v1 fatcat:kib67ldmpzeg7aklkfuawvhl2m

A practical relativistic theory of three-body scattering

D. D. Brayshaw
1975 Physical Review D, Particles and fields  
A natural and unambiguous generalization of the boundary condition formalism previously proposed by this author is shown to result in a practical set of equations for describing relativistic threeparticle  ...  Applied to the O-and lstates of the 37r system (I = 0, 1, 2), they yield the 7r and w as natural consequences of the 7r-7~ s-and p-wave phases ; there are no spurious predictions .  ...  values of &.One thus proceeds by approximating the integral as a finite sum through the introduction of appropriate Gaussian rjoints qi, and weights hi, converting 17 Eq. (87) into a finite matrix equation  ... 
doi:10.1103/physrevd.11.2583 fatcat:66jkjoeksra77lofcbixcmk3zq
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