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Solving Discrete Logarithms on a 170-Bit MNT Curve by Pairing Reduction
[chapter]
2017
Lecture Notes in Computer Science
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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]
2016
arXiv
pre-print
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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
2006
Artificial Intelligence
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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
2016
Journal of Optimization Theory and Applications
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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]
1997
DIMACS Series in Discrete Mathematics and Theoretical Computer Science
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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
2010
2010 12th International Asia-Pacific Web Conference
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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
2017
International Journal of Computer Applications
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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]
2009
Algorithms and Theory of Computation Handbook, Second Edition, Volume 1
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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]
2013
arXiv
pre-print
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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
2020
Journal of automated reasoning
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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]
2018
Lecture Notes in Computer Science
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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
2017
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
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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]
1998
Lecture Notes in Computer Science
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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
1987
Annual Review of Computer Science
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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]
2019
arXiv
pre-print
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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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