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Solving Discrete Logarithms on a 170-Bit MNT Curve by Pairing Reduction [chapter]

Aurore Guillevic, François Morain, Emmanuel Thomé
2017 Lecture Notes in Computer Science  
We report a discrete logarithm computation in the group of points of this curve by a pairing reduction, using only a moderate amount of computing power.  ...  In [28] , for a supersingular curve over F 3 97 , the small characteristic allowed the use of the Function Field Sieve algorithm [1], and the composite extension degree was also a very useful property.  ...  A particular element which lifts conveniently in K f is the common root t of both polynomials.  ... 
doi:10.1007/978-3-319-69453-5_30 fatcat:qhxg3rrwe5c37lratgpzk5jihy

Solving discrete logarithms on a 170-bit MNT curve by pairing reduction [article]

Aurore Guillevic, Emmanuel Thomé
2016 arXiv   pre-print
As a computational example, we solve the DLP on a 170-bit MNT curve, by exploiting the pairing embedding to a 508-bit, degree-3 extension of the base field.  ...  Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic.  ...  A particular element which lifts conveniently in K f is the common root t of both polynomials.  ... 
arXiv:1605.07746v2 fatcat:kwaeic6iqrfw3ekowzhojf6rru

Backward-chaining evolutionary algorithms

Riccardo Poli, William B. Langdon
2006 Artificial Intelligence  
Starting from some simple observations on a popular selection method in Evolutionary Algorithms (EAs)-tournament selection-we highlight a previously-unknown source of inefficiency.  ...  Since fitness evaluation typically dominates the resources needed to solve any non-trivial problem, these savings translate into a reduction in computer time.  ...  The reviewers and the co-editor-in-chief in charge of this manuscript are also warmly thanked for their help in improving it.  ... 
doi:10.1016/j.artint.2006.04.003 fatcat:epsornnja5aw7mnoikcudxiut4

A Constraint-Reduced Algorithm for Semidefinite Optimization Problems with Superlinear Convergence

Sungwoo Park
2016 Journal of Optimization Theory and Applications  
Constraint reduction is an essential method because the computational cost of the interior point methods can be effectively saved.  ...  We first develop a constraintreduced algorithm for semidefinite programming having both polynomial global and superlinear local convergences.  ...  we can avoid duplicate computations for off-diagonal elements of symmetric A i .  ... 
doi:10.1007/s10957-016-0917-y fatcat:7wxomdspe5ezrobhupuljiifs4

Concerning the NJ algorithm and its unweighted version, UNJ [chapter]

Olivier Gascuel
1997 DIMACS Series in Discrete Mathematics and Theoretical Computer Science  
Rzhetsky and Nei (1993) provide a thorough justification of the ME principle.  ...  The length of a valued tree is the sum of the lengths (valuations) of its edges, and within the ME principle, these are estimated using the least-squares criterion, without the positivity constraint.  ...  each element δ ij is an estimate or a measure, generally imperfect, of the distance d ij .  ... 
doi:10.1090/dimacs/037/09 dblp:conf/dimacs/Gascuel96 fatcat:ku3oe2s6yre6bk2nlltfb7anu4

A Space and Time Efficient Algorithm for SimRank Computation

Weiren Yu, Xuemin Lin, Jiajin Le
2010 2010 12th International Asia-Pacific Web Conference  
In addition, we extend the similarity transition matrix to prevent random surfers getting stuck, and devise a pruning technique to eliminate impractical similarities for each iteration.  ...  In this paper, we propose novel optimization techniques such that each iteration takes O (min {n · m, n r }) time and O (n + m) space, where m is the number of edges in a web-graph model and r ≤ log 2  ...  We also used three real-life Wikipedia category graphs (exported in 2009) to investigate the effectiveness of the our algorithms.  ... 
doi:10.1109/apweb.2010.42 dblp:conf/apweb/YuLL10 fatcat:ktzfyq5jv5ecdgrpn4zfczqoue

An Improved Frame Level Redundancy Scrubbing Algorithm for SRAM based FPGA

O. E., K. A., A. T.
2017 International Journal of Computer Applications  
The performance of the improved FLR algorithm was compared with that of the existing FLR algorithm using error correction time and energy consumption as metrics.  ...  The use of Static Random Access Memory (SRAM) based Field Programmable Gate Array (FPGA) in critical applications has been considered a solution in space and avionics domain due to its flexibility in achieving  ...  International Journal of Computer Applications (0975 -8887) Volume 170 -No.5, July 2017  ... 
doi:10.5120/ijca2017914844 fatcat:mqllhij3zrfzzkezjdeid4cafu

Algebraic and Numerical Algorithms [chapter]

Ioannis Emiris, Victor Pan, Elias Tsigaridas
2009 Algorithms and Theory of Computation Handbook, Second Edition, Volume 1  
Then the matrix M contains a single variable w and is denoted M (w).  ...  Using the fast algorithms for polynomial remainder sequences evaluation (243; 170) we can prove a O B (d 4 τ 2 ) bound for the overall algorithm (71; 81; 98) and that in the same time we can also compute  ... 
doi:10.1201/9781584888239-c17 fatcat:khegroceujdbpc3ukvlv6s3j4i

Chapter 10: Algebraic Algorithms [article]

Ioannis Z. Emiris, Victor Y. Pan, Elias P. Tsigaridas
2013 arXiv   pre-print
Diaz-Herrera, editors, covers Algebraic Algorithms, both symbolic and numerical, for matrix computations and root-finding for polynomials and systems of polynomials equations.  ...  We cover part of these large subjects and include basic bibliography for further study.  ...  Much like a polynomial remainder process, the process of polynomial reduction involves subtracting a multiple of one polynomial from another to obtain a smaller degree result [50, 105, 127] .  ... 
arXiv:1311.3731v1 fatcat:whtgwztbmbgqbl44s4e663oulu

Formalizing the LLL Basis Reduction Algorithm and the LLL Factorization Algorithm in Isabelle/HOL

René Thiemann, Ralph Bottesch, Jose Divasón, Max W. Haslbeck, Sebastiaan J. C. Joosten, Akihisa Yamada
2020 Journal of automated reasoning  
The LLL basis reduction algorithm was the first polynomial-time algorithm to compute a reduced basis of a given lattice, and hence also a short vector in the lattice.  ...  We additionally integrate one application of LLL, namely a verified factorization algorithm for univariate integer polynomials which runs in polynomial time.  ...  Sebastiaan is now working at University of Twente, the Netherlands, and supported by the NWO VICI 639.023.710 Mercedes project.  ... 
doi:10.1007/s10817-020-09552-1 pmid:32831440 pmcid:PMC7413592 fatcat:fhfgozhs5zhvzg7zfooxpdiina

A Formalization of the LLL Basis Reduction Algorithm [chapter]

Jose Divasón, Sebastiaan Joosten, René Thiemann, Akihisa Yamada
2018 Lecture Notes in Computer Science  
The LLL basis reduction algorithm was the first polynomialtime algorithm to compute a reduced basis of a given lattice, and hence also a short vector in the lattice.  ...  We additionally integrate one application of LLL, namely a verified factorization algorithm for univariate integer polynomials which runs in polynomial time.  ...  Some of the research was conducted while Sebastiaan Joosten and Akihisa Yamada were working in the University of Innsbruck.  ... 
doi:10.1007/978-3-319-94821-8_10 fatcat:fpazlnxfyrhvzltnl23t6u36e4

Decidability of the Membership Problem for 2 × 2 integer matrices

Igor Potapov, Pavel Semukhin
2017 Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms  
Our algorithm relies on a translation of numerical problems on matrices into combinatorial problems on words.  ...  It also makes use of some algebraic properties of well-known subgroups of GL(2, Z) and various new techniques and constructions that help to convert matrix equations into the emptiness problem for intersection  ...  The next steps of the algorithm can be done in polynomial time.  ... 
doi:10.1137/1.9781611974782.12 dblp:conf/soda/PotapovS17 fatcat:ghupg4wybvczzdy3stp53bgeni

On finding small solutions of modular multivariate polynomial equations [chapter]

Charanjit S. Jutla
1998 Lecture Notes in Computer Science  
This algorithm is an extension of Coppersmith's algorithm [2] , which guarantees only one polynomial equation.  ...  We show that there is an algorithm which determines c(~ 1) integer polynomial equations (in m variables) of total degree polynomial in cmklog N, in time polynomial in craklog N, such that each of the equations  ...  When dealing with multivariate polynomials, the dimension of the matrix involved in the basis reduction starts becoming rather large.  ... 
doi:10.1007/bfb0054124 fatcat:brktftrufnhebd2gxwy6n4ev2i

Computer Algebra Algorithms

E Kaltofen
1987 Annual Review of Computer Science  
A reduction from factoring in Q(θ )[x]tofactoring in Q[x]isgiv en(Kronecker 1882 [97]; Trager 1976 [170]; Landau 1985) [100].  ...  (a) The results are symbolic rather than numerical, as the typical example of the inversion of a symbolic matrix demonstrates.  ... 
doi:10.1146/annurev.cs.02.060187.000515 fatcat:5ogho43razbdtchftgrhxvghrm

Assessment of localized and randomized algorithms for electronic structure [article]

Jonathan E. Moussa, Andrew D. Baczewski
2019 arXiv   pre-print
Using large copper clusters in a minimal-basis semiempirical model as our reference system, we study the costs of these algorithms relative to a conventional cubic-scaling algorithm using matrix diagonalization  ...  and a recent quadratic-scaling algorithm using sparse matrix factorization and rational function approximation.  ...  Thus an off-diagonal spatial decay of density matrix elements is directly proportional to a reduction of observable error bounds with increasing r max .  ... 
arXiv:1812.05264v3 fatcat:bqdzj255mraepedmwozva2lzze
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