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On the low hamming weight discrete logarithm problem for nonadjacent representations

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. ...

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

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. ...

##
###
Graph Powers, Delsarte, Hoffman, Ramsey, and Shannon

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. ...

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

2012
*
arXiv
*
pre-print

Another digital regularity is suggested here,

arXiv:math/0612627v17
fatcat:chwrddxhrbdllf73twmls3m2ci
*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. ...##
###
Quantum Algorithms for Scientific Computing and Approximate Optimization
[article]

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*...

##
###
Fast point multiplication on Koblitz curves: Parallelization method and implementations

2009
*
Microprocessors and microsystems
*

They compute point multiplications

doi:10.1016/j.micpro.2008.08.002
fatcat:5mlvg4ysvfe3rdsesgb7n6qm7q
*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 ...##
###
Limits to parallel computation: P-completeness theory

1996
*
ChoiceReviews
*

This book is an introduction to

doi:10.5860/choice.33-3959
fatcat:qjoueeu225gr7jvwdf6gkoxfbq
*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. ...##
###
The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
[article]

2018
*
arXiv
*
pre-print

We discuss five

arXiv:1706.05975v3
fatcat:rtwl6jd77zbtbklqco4wxym5ly
*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. ...##
###
Cold Boot Attacks on the Supersingular Isogeny Key Encapsulation (SIKE) Mechanism

2020
*
Applied Sciences
*

This research paper evaluates

doi:10.3390/app11010193
fatcat:uschxvs6kbaafadyfy4ai2qmde
*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*. ...##
###
The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg

2019
*
Bulletin of the American Mathematical Society
*

Going from Z 2 to other coefficient groups involves only

doi:10.1090/bull/1653
fatcat:vby5jazp2zd6lc2ev3qqgxm2cq
*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. ...##
###
Computational Complexity of Some Quantum Theories in 1+1 Dimensions
[article]

2015
*
arXiv
*
pre-print

We study

arXiv:1512.09243v1
fatcat:y6yxujvibbftvplgliltp3gvii
*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*. ...##
###
Efficient implementation of ideal lattice-based cryptography

2017
*
it - Information Technology
*

AbstractAlmost all practically relevant asymmetric cryptosystems like RSA or ECC are either based

doi:10.1515/itit-2017-0030
fatcat:mpmamskk25h3lbyshy4rfd4y4y
*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. ...##
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Efficient and side-channel-aware implementations of elliptic curve cryptosystems over prime fields

2010
*
IET Information Security
*

To our knowledge

doi:10.1049/iet-ifs.2009.0038
fatcat:2pgbfcss3ve6vnwdnwpfhkd35m
*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. ...##
###
Dynamical directions in numeration

2006
*
Annales de l'Institut Fourier
*

defined

doi:10.5802/aif.2233
fatcat:5ahms6x5jzdb7mynm74pmyhsve
*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 ...##
###
Extraction of spatio-temporal primitives of emotional body expressions

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 ...

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