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

Sungwook Kim, Jung Hee Cheon
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.  ... 
doi:10.1007/978-3-540-78440-1_19 dblp:conf/pkc/KimC08 fatcat:qkrbd7i7ojgbjjhq7ntzk46md4

Parameterized Splitting Systems for the Discrete Logarithm

Sungwook Kim, Jung Hee Cheon
2010 IEEE Transactions on Information Theory  
Hoffstein 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] .  ... 
doi:10.1109/tit.2010.2044071 fatcat:5scrnflxcnh4pnxxxxrtqz5mhq

On the Bounded Sum-of-digits Discrete Logarithm Problem in Kummer and Artin-Schreier Extensions [article]

Qi Cheng
2003 arXiv   pre-print
In this paper, we study 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.  ... 
arXiv:math/0311120v1 fatcat:6guf7oj7bjaxli6vercrofc6fy

On the Bounded Sum-of-Digits Discrete Logarithm Problem in Finite Fields

Qi Cheng
2005 SIAM journal on computing (Print)  
We then show that 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.  ... 
doi:10.1137/s0097539704446037 fatcat:wxmpgefqkbbg7nnxgxyfmdjeke

On the Bounded Sum-of-Digits Discrete Logarithm Problem in Finite Fields [chapter]

Qi Cheng
2004 Lecture Notes in Computer Science  
We then show that 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.  ... 
doi:10.1007/978-3-540-28628-8_12 fatcat:yjt5sj3i7nhppfqgmfbzp4x47e

Rate Distortion Behavior of Sparse Sources

Claudio Weidmann, Martin Vetterli
2012 IEEE Transactions on Information Theory  
For strictly sparse binary sources 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.  ... 
doi:10.1109/tit.2012.2201335 fatcat:i7x3mjprujgdvhtb6o4bx6a4q4

Perfect nonlinear functions and cryptography

Céline Blondeau, Kaisa Nyberg
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.  ... 
doi:10.1016/j.ffa.2014.10.007 fatcat:5ixuv7o3fbbdzaxrjuysskbpim

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

Reza Hooshmand, Masoumeh Koochak Shooshtari, Mohammad Reza Aref
2017 arXiv   pre-print
Polar codes are novel 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 .  ... 
arXiv:1712.07672v1 fatcat:tbwh5oagvze3bixmk4rdl2qdey

Quantum Algorithms for Scientific Computing and Approximate Optimization [article]

Stuart Hadfield
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.  ... 
arXiv:1805.03265v1 fatcat:7ycpl3byjrg73kn4jpzg5ajiwy

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

B. Sunar
2004 IEEE transactions on computers  
We present 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.  ... 
doi:10.1109/tc.2004.52 fatcat:3xzdahqz35bb7pdccamazbgpni

Sub-banded reconstructed phase spaces for speech recognition

Kevin M. Indrebo, Richard J. Povinelli, Michael T. Johnson
2006 Speech Communication  
Results also demonstrate that 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] .  ... 
doi:10.1016/j.specom.2004.12.002 fatcat:dzbpr6ld7rfntjwgp3tgpba4u4

Optimal Execution with Nonlinear Transient Market Impact

Gianbiagio Curato, Jim Gatheral, Fabrizio Lillo
2014 Social Science Research Network  
We study 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.  ... 
doi:10.2139/ssrn.2539240 fatcat:frfr55vk7bbarbkh44fqru33li

Optimal execution with non-linear transient market impact

Gianbiagio Curato, Jim Gatheral, Fabrizio Lillo
2016 Quantitative finance (Print)  
We study 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.  ... 
doi:10.1080/14697688.2016.1181274 fatcat:6habh2aubnbdrjv2ndcicq6zzi

Record dynamics of evolving metastable systems: theory and applications

Paolo Sibani, Stefan Boettcher, Henrik Jeldtoft Jensen
2021 European Physical Journal B : Condensed Matter Physics  
Record Dynamics (RD) deals 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  ... 
doi:10.1140/epjb/s10051-020-00039-x fatcat:ym4k6o7rlvhovcc46dl6srkpo4

Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape [article]

Vadim N. Smelyanskiy, Konstyantyn Kechedzhi, Sergio Boixo, Sergei V. Isakov, Hartmut Neven, Boris Altshuler
2018 arXiv   pre-print
Given an energy function E(z) of 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. .  ... 
arXiv:1802.09542v2 fatcat:sczjo45trrgbtiwe6a3sdjjoqa
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