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On the low hamming weight discrete logarithm problem for nonadjacent representations

J.A. Muir, D.R. Stinson
2005 Applicable Algebra in Engineering, Communication and Computing  
The security is studied by examining a related discrete logarithm problem, the topic of this paper.  ...  We describe an algorithm to solve the relevant discrete logarithm problem in time that is approximately the square root of the search space.  ...  Acknowledgements Research of DRS is supported by the Natural Sciences and Engineering Research Council of Canada through the grant NSERC-RGPIN #203114-02.  ... 
doi:10.1007/s00200-005-0187-7 fatcat:qfgfo4b3hferxghom2huw5n6ca

Improving Schrödinger Equation Implementations with Gray Code for Adiabatic Quantum Computers [article]

Chia Cheng Chang, Kenneth S. McElvain, Ermal Rrapaj, Yantao Wu
2022 arXiv   pre-print
For the Hamming distance 2 Gray code, the evolution starts with the transverse Hamiltonian before introducing penalties such that the low lying spectrum reproduces the energy levels of the Laplacian.  ...  for all encodings.  ...  Then, one diagonalizes the resulting matrix, either completely, or for very large problems, uses techniques such as the Lanczos algorithm to find low-lying eigenstates and eigenvalues.  ... 
arXiv:2103.08056v4 fatcat:iwugpl47pzg4jhycn7xoqyafxe

Graph Powers, Delsarte, Hoffman, Ramsey, and Shannon

Noga Alon, Eyal Lubetzky
2007 SIAM Journal on Discrete Mathematics  
For precise bounds on some graphs, we apply Delsarte's linear programming bound and Hoffman's eigenvalue bound.  ...  Finally, we show that for any nontrivial graph G, one can point out specific induced subgraphs of large p-powers of G with neither a large clique nor a large independent set.  ...  The authors would like to thank Simon Litsyn and Benny Sudakov for useful discussions.  ... 
doi:10.1137/060657893 fatcat:iqyimya4lvc5nndjr7ebkthvlu

Towards A Better Understanding Of The Leading Digits Phenomena [article]

Alex Ely Kossovsky
2012 arXiv   pre-print
Another digital regularity is suggested here, one that is found in logarithmic as well as non-logarithmic random data sets.  ...  the distributions generating the parameters are themselves logarithmic.  ...  The lower the lambda the more logarithmic it is for a given mu. Hence for a logarithmic behavior here we need to have a low ratio of lambda/mu.  ... 
arXiv:math/0612627v17 fatcat:chwrddxhrbdllf73twmls3m2ci

Quantum Algorithms for Scientific Computing and Approximate Optimization [article]

Stuart Hadfield
2018 arXiv   pre-print
problems and low-resource implementations on near-term quantum devices.  ...  The first three deal with quantum algorithms for computational problems in science and engineering, including quantum simulation of physical systems.  ...  We employ a unary one-hot encoding for each k-dit, consisting of the k-many Hamming weight 1 bit strings on k bits, {100 . . . , 010 . . . , . . . }, in which the position of the single 1 indicates the  ... 
arXiv:1805.03265v1 fatcat:7ycpl3byjrg73kn4jpzg5ajiwy

Fast point multiplication on Koblitz curves: Parallelization method and implementations

Kimmo Järvinen, Jorma Skyttä
2009 Microprocessors and microsystems  
They compute point multiplications on average in 4.9 ls, 8.1 ls, and 12.1 ls on the standardized curves NIST K-163, K-233, and K-283, respectively, in an Altera Stratix II FPGA.  ...  FPGA implementations are described showing the practical feasibility of our method.  ...  (1) We present a simple and efficient method for speeding up Koblitz  ... 
doi:10.1016/j.micpro.2008.08.002 fatcat:5mlvg4ysvfe3rdsesgb7n6qm7q

Limits to parallel computation: P-completeness theory

1996 ChoiceReviews  
This book is an introduction to the rapidly growing theory of Pcompleteness -the branch of complexity theory that focuses on identifying the "hardest" problems in the class P of problems solvable in polynomial  ...  This state of affairs is succinctly expressed as the following question: Does P equal NC ? PREFACE ix the best known parallel algorithms for the problem.  ...  Acknowledgments The numbers in parentheses at the end of each entry in the bibliography are the page numbers on which that item is referenced.  ... 
doi:10.5860/choice.33-3959 fatcat:qjoueeu225gr7jvwdf6gkoxfbq

The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg [article]

Jesus A. De Loera, Xavier Goaoc, Frédéric Meunier, Nabil Mustafa
2018 arXiv   pre-print
We discuss five discrete results: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carath\'eodory, Helly, and Tverberg from combinatorial geometry.  ...  He is grateful to the labex BEZOUT and the CERMICS research center atÉcole National des Ponts et Chaussées for the support received, and the enjoyable and welcoming environment in which the topics in this  ...  The authors are truly grateful to the two anonymous referees who provided a very large and very detailed set of comments, insights, and corrections.  ... 
arXiv:1706.05975v3 fatcat:rtwl6jd77zbtbklqco4wxym5ly

Cold Boot Attacks on the Supersingular Isogeny Key Encapsulation (SIKE) Mechanism

Ricardo Villanueva-Polanco, Eduardo Angulo-Madrid
2020 Applied Sciences  
This research paper evaluates the feasibility of cold boot attacks on the Supersingular Isogeny Key Encapsulation (SIKE) mechanism.  ...  Furthermore, we present a dedicated key-recovery algorithm for SIKE in this setting and show that the key recovery algorithm works for all the parameter sets recommended for this scheme.  ...  The first one is the windowed nonadjacent form (wNAF) representation, and the second is the comb-based representation.  ... 
doi:10.3390/app11010193 fatcat:uschxvs6kbaafadyfy4ai2qmde

The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg

Jesús A. De Loera, Xavier Goaoc, Frédéric Meunier, Nabil H. Mustafa
2019 Bulletin of the American Mathematical Society  
Going from Z 2 to other coefficient groups involves only one technical complication: the definition of ∂ i involves some sign bookkeeping, so as to ensure that ∂ i−1 • ∂ i = 0; see [288] for details.  ...  In particular, if K is a single vertex, then all its homology groups are trivial except the 0th one.  ...  Acknowledgments The authors are truly grateful to the two anonymous referees who provided a very large and very detailed set of comments, insights, and corrections.  ... 
doi:10.1090/bull/1653 fatcat:vby5jazp2zd6lc2ev3qqgxm2cq

Computational Complexity of Some Quantum Theories in 1+1 Dimensions [article]

Saeed Mehraban
2015 arXiv   pre-print
We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories.  ...  We prove that additive approximation to single amplitudes of these models can be obtained by the one-clean-qubit model, if no initial superpositions are allowed.  ...  We establish the proof for the case where the swaps are adjacent ones, the proof for nonadjacent swaps is immediate since adjacent swaps can simulate non-adjacent ones.  ... 
arXiv:1512.09243v1 fatcat:y6yxujvibbftvplgliltp3gvii

Efficient implementation of ideal lattice-based cryptography

Thomas Pöppelmann
2017 it - Information Technology  
AbstractAlmost all practically relevant asymmetric cryptosystems like RSA or ECC are either based on the hardness of factoring or on the hardness of the discrete logarithm problem.  ...  However, both problems could be solved efficiently on a large enough quantum computer.  ...  low hamming weight representation and thus a minimal number of additions.  ... 
doi:10.1515/itit-2017-0030 fatcat:mpmamskk25h3lbyshy4rfd4y4y

Efficient and side-channel-aware implementations of elliptic curve cryptosystems over prime fields

D. Karakoyunlu, F.K. Gurkaynak, B. Sunar, Y. Leblebici
2010 IET Information Security  
To our knowledge the authors present the first hardware implementation for the Edwards formulation of elliptic curves.  ...  Elliptic curve cryptosystems (ECCs) are utilised as an alternative to traditional public-key cryptosystems, and are more suitable for resource-limited environments because of smaller parameter size.  ...  Acknowledgments The authors would like to express their thanks Dr. Marcelo Kaihara and Prof. Arjen Lenstra for their support, assistance and inspiration during the implementation period of this work.  ... 
doi:10.1049/iet-ifs.2009.0038 fatcat:2pgbfcss3ve6vnwdnwpfhkd35m

Dynamical directions in numeration

Guy Barat, Valérie Berthé, Pierre Liardet, Jörg Thuswaldner
2006 Annales de l'Institut Fourier  
defined on them.  ...  The exposition is unified by the fibred numeration system concept. Many examples are discussed.  ...  Acknowledgements We would like to thank the anonymous referees of the present paper for their valuable remarks which have significantly improved the readability of the paper and the exposition of the results  ... 
doi:10.5802/aif.2233 fatcat:5ahms6x5jzdb7mynm74pmyhsve

Extraction of spatio-temporal primitives of emotional body expressions

Lars Omlor, Martin A. Giese
2007 Neurocomputing  
representations for new words can be constructed based on old representations.  ...  In this case the tuning problem reduces to a simple curve fitting problem for each neuron whereby the known tuning curve data is directly incorporated into the model while the synaptic weights are set  ... 
doi:10.1016/j.neucom.2006.10.100 fatcat:esivhljzsbcihdl5qbp756josu
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