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A Parameterized Splitting System and Its Application to the Discrete Logarithm Problem with Low Hamming Weight Product Exponents
[chapter]

*
Public Key Cryptography – PKC 2008
*

*A*

*low*

*Hamming*

*weight*

*product*(LHWP)

*exponent*is used

*to*increase

*the*efficiency of cryptosystems based on

*the*

*discrete*

*logarithm*

*problem*(DLP). ... In this paper, we introduce

*a*new tool, called

*a*

*Parameterized*

*Splitting*

*System*,

*to*analyze

*the*security of

*the*DLP

*with*LHWP

*exponents*. ...

*The*authors would like

*to*thank Martijn Stam

*and*

*the*anonymous referees for valuable comments.

*The*first author also would like

*to*thank Namsu Jho for helpful discussions. ...

##
###
Parameterized Splitting Systems for the Discrete Logarithm

2010
*
IEEE Transactions on Information Theory
*

Hoffstein

doi:10.1109/tit.2010.2044071
fatcat:5scrnflxcnh4pnxxxxrtqz5mhq
*and*Silverman suggested*the*use of*low**Hamming**weight**product*(LHWP)*exponents**to*accelerate group exponentiation while maintaining*the*security level. ... We show that*it*yields an algorithm for*the**discrete**logarithm**problem*(DLP)*with*LHWP*exponents**with*lower complexity than that of any previously known algorithms. ...*To*resist previous attacks*and*achieve*a*greater speed-up, Hoffstein*and*Silverman suggested*the*use of*low**Hamming**weight**product*(LHWP)*exponents*[11] . ...##
###
On the Bounded Sum-of-digits Discrete Logarithm Problem in Kummer and Artin-Schreier Extensions
[article]

2003
*
arXiv
*
pre-print

In this paper, we study

arXiv:math/0311120v1
fatcat:6guf7oj7bjaxli6vercrofc6fy
*the**discrete**logarithm**problem*in*the*finite fields _q^n where n|q-1.*The*field is called*a*Kummer field or*a*Kummer extension of _q. ... function*and*w is*the*bound on*the*q-ary sum-of-digits of*the**exponent*. ... Parameters of*low**Hamming**weight*, or more generally, of small sum-of-digits, offer some remedy. Using them speeds up*the**system*while seems*to*keep*the*security intact. ...##
###
On the Bounded Sum-of-Digits Discrete Logarithm Problem in Finite Fields

2005
*
SIAM journal on computing (Print)
*

We then show that

doi:10.1137/s0097539704446037
fatcat:wxmpgefqkbbg7nnxgxyfmdjeke
*the**problem*is solvable in random polynomial time for most of*the**exponent*e*with*Sq(e) < 1.32n, by exploring an interesting connection between*the**discrete**logarithm**problem**and**the*... We also prove that in*the*field F q q−1 ,*the*bounded sum-of-digits*discrete**logarithm**with*respect*to*g can be computed in random time O(f (w) log 4 (q q−1 )), where f is*a*subexponential function*and*... Parameters of*low**Hamming**weight*, or more generally, of small sum-of-digits, offer some remedy. Using them speeds up*the**system*while seeming*to*keep*the*security intact. ...##
###
On the Bounded Sum-of-Digits Discrete Logarithm Problem in Finite Fields
[chapter]

2004
*
Lecture Notes in Computer Science
*

We then show that

doi:10.1007/978-3-540-28628-8_12
fatcat:yjt5sj3i7nhppfqgmfbzp4x47e
*the**problem*is solvable in random polynomial time for most of*the**exponent*e*with*Sq(e) < 1.32n, by exploring an interesting connection between*the**discrete**logarithm**problem**and**the*... We also prove that in*the*field F q q−1 ,*the*bounded sum-of-digits*discrete**logarithm**with*respect*to*g can be computed in random time O(f (w) log 4 (q q−1 )), where f is*a*subexponential function*and*... Parameters of*low**Hamming**weight*, or more generally, of small sum-of-digits, offer some remedy. Using them speeds up*the**system*while seeming*to*keep*the*security intact. ...##
###
Rate Distortion Behavior of Sparse Sources

2012
*
IEEE Transactions on Information Theory
*

For strictly sparse binary sources

doi:10.1109/tit.2012.2201335
fatcat:i7x3mjprujgdvhtb6o4bx6a4q4
*with**Hamming*distortion, is shown*to*be almost linear. ...*The*former are versatile models for sparse data, which in particular allow*to*bound high-rate compression performance of*a*scalar mixture compared*to**a*corresponding unmixed transform coding*system*. ... ACKNOWLEDGMENT*The*authors wish*to*thank E. ...##
###
Perfect nonlinear functions and cryptography

2015
*
Finite Fields and Their Applications
*

*To*illustrate

*the*use of PN

*and*APN functions in practice, we discuss examples of ciphers

*and*their resistance

*to*differential attacks. ... We recall how

*the*links

*with*other mathematical concepts have accelerated

*the*search on PN

*and*APN functions. ... Acknowledgments

*The*authors wish

*to*thank

*the*anonymous reviewers for correcting many errors in

*the*manuscript

*and*giving insightful comments for improving

*the*presentation of

*the*paper. ...

##
###
PKC-PC: A Variant of the McEliece Public Key Cryptosystem based on Polar Codes
[article]

2017
*
arXiv
*
pre-print

Polar codes are novel

arXiv:1712.07672v1
fatcat:tbwh5oagvze3bixmk4rdl2qdey
*and*efficient error correcting codes*with**low*encoding*and*decoding complexities. ... Moreover,*it*is indicated that*the*security of*the*PKC-PC is reduced*to*solve NP-complete*problems*. ... Since*the**Hamming**weight*of intentional error vector is less than ,*the*attacker performs*a**low**weight*word search algorithm*to*detect . ...##
###
Quantum Algorithms for Scientific Computing and Approximate Optimization
[article]

2018
*
arXiv
*
pre-print

*The*first three deal

*with*quantum algorithms for computational

*problems*in science

*and*engineering, including quantum simulation of physical

*systems*. ... In this thesis we consider

*the*

*application*of quantum computers

*to*scientific computing

*and*combinatorial optimization. We study five

*problems*. ... ,

*to*between N 5

*to*N 7 ,

*with*

*exponent*depending on

*the*particular

*problem*representation

*and*details. ...

##
###
A generalized method for constructing subquadratic complexity GF(2/sup k/) multipliers

2004
*
IEEE transactions on computers
*

We present

doi:10.1109/tc.2004.52
fatcat:3xzdahqz35bb7pdccamazbgpni
*a*recursive construction technique that extends any d point multiplier into an n ¼ d k point multiplier*with*area that is subquadratic*and*delay that is*logarithmic*in*the*bit-length n. ... We present*a*thorough analysis that establishes*the*exact space*and*time complexities of these multipliers. ... ACKNOWLEDGMENTS This material is based upon work supported by*the*US National Science Foundation under Grant No. ANI-0112889. ...##
###
Sub-banded reconstructed phase spaces for speech recognition

2006
*
Speech Communication
*

Results also demonstrate that

doi:10.1016/j.specom.2004.12.002
fatcat:dzbpr6ld7rfntjwgp3tgpba4u4
*the*proposed phoneme classification*system*is competitive*with*state-of-*the*-art approaches. iii Hands-free computer control*systems*allow users*to*execute basic operations ... Several methods for*the*combination of*the*sub-band classifications are examined,*and**it*is found that an un-*weighted*linear combination produces classification accuracies that are significantly higher ... Traditional*Systems*Traditional ASR*systems*use front-end acoustic*parameterization*methods that are based on*a*switched-excitation linear source-filter model of human speech*production*[1] . ...##
###
Optimal Execution with Nonlinear Transient Market Impact

2014
*
Social Science Research Network
*

We study

doi:10.2139/ssrn.2539240
fatcat:frfr55vk7bbarbkh44fqru33li
*the**problem*of*the*optimal execution of*a*large trade in*the*presence of nonlinear transient impact. ... We find that*the*optimal solution is front loaded for concave impact*and*that*its*expected cost is significantly lower than that of conventional strategies. ...*A**Discrete*Homotopy Analysis Method*To*apply*HAM**to*our*problem*, we need*to*compute*the*definite integrals (3.17) , which seem*to*be analytically intractable. ...##
###
Optimal execution with non-linear transient market impact

2016
*
Quantitative finance (Print)
*

We study

doi:10.1080/14697688.2016.1181274
fatcat:6habh2aubnbdrjv2ndcicq6zzi
*the**problem*of*the*optimal execution of*a*large trade in*the*presence of nonlinear transient impact. ... We find that*the*optimal solution is front loaded for concave impact*and*that*its*expected cost is significantly lower than that of conventional strategies. ...*A**Discrete*Homotopy Analysis Method*To*apply*HAM**to*our*problem*, we need*to*compute*the*definite integrals (3.17) , which seem*to*be analytically intractable. ...##
###
Record dynamics of evolving metastable systems: theory and applications

2021
*
European Physical Journal B : Condensed Matter Physics
*

Record Dynamics (RD) deals

doi:10.1140/epjb/s10051-020-00039-x
fatcat:ym4k6o7rlvhovcc46dl6srkpo4
*with*complex*systems*evolving through*a*sequence of metastable stages. ...*It*then outlines*the*Poissonian nature of records events in white noise time-series,*and*connects*it**to**the*statistics of quakes in metastable hierarchical*systems*, arguing that*the*relaxation effects ...*It*is equally clear that*a**logarithmic*trend cannot continue indefinitely*and*that*the*growth law f = f 0 (1 − t −α ), where*the**exponent*α is*a*positive number close*to*zero, grows as*a**logarithm*for ...##
###
Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape
[article]

2018
*
arXiv
*
pre-print

Given an energy function E(z) of

arXiv:1802.09542v2
fatcat:sczjo45trrgbtiwe6a3sdjjoqa
*a*binary optimization*problem**and**a*bit-string z_i*with*atypically*low*energy, our goal is*to*find other bit-strings*with*energies within*a*narrow window around E(z_i). ... Under certain conditions,*the*band of*the**system*eigenstates*splits*into mini-bands of non-ergodic delocalized states, whose width obeys*a*heavy-tailed distribution directly related*to*that of PT runtimes ...*The*U.S. Government is authorized*to*reproduce*and*distribute reprints for Governmental purpose notwithstanding any copyright annotation thereon. . ...
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