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

2017
*
Lecture Notes in Computer Science
*

We report

doi:10.1007/978-3-319-69453-5_30
fatcat:qhxg3rrwe5c37lratgpzk5jihy
*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*. ...##
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Solving discrete logarithms on a 170-bit MNT curve by pairing reduction
[article]

2016
*
arXiv
*
pre-print

As

arXiv:1605.07746v2
fatcat:kwaeic6iqrfw3ekowzhojf6rru
*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*. ...##
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Backward-chaining evolutionary algorithms

2006
*
Artificial Intelligence
*

Starting from some simple observations on

doi:10.1016/j.artint.2006.04.003
fatcat:epsornnja5aw7mnoikcudxiut4
*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. ...##
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A Constraint-Reduced Algorithm for Semidefinite Optimization Problems with Superlinear Convergence

2016
*
Journal of Optimization Theory and Applications
*

Constraint

doi:10.1007/s10957-016-0917-y
fatcat:7wxomdspe5ezrobhupuljiifs4
*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 . ...##
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Concerning the NJ algorithm and its unweighted version, UNJ
[chapter]

1997
*
DIMACS Series in Discrete Mathematics and Theoretical Computer Science
*

Rzhetsky and Nei (1993) provide

doi:10.1090/dimacs/037/09
dblp:conf/dimacs/Gascuel96
fatcat:ku3oe2s6yre6bk2nlltfb7anu4
*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 . ...##
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A Space and Time Efficient Algorithm for SimRank Computation

2010
*
2010 12th International Asia-Pacific Web Conference
*

In addition, we extend the similarity transition

doi:10.1109/apweb.2010.42
dblp:conf/apweb/YuLL10
fatcat:ktzfyq5jv5ecdgrpn4zfczqoue
*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*. ...##
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An Improved Frame Level Redundancy Scrubbing Algorithm for SRAM based FPGA

2017
*
International Journal of Computer Applications
*

The performance

doi:10.5120/ijca2017914844
fatcat:mqllhij3zrfzzkezjdeid4cafu
*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 ...##
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Algebraic and Numerical Algorithms
[chapter]

2009
*
Algorithms and Theory of Computation Handbook, Second Edition, Volume 1
*

Then the

doi:10.1201/9781584888239-c17
fatcat:khegroceujdbpc3ukvlv6s3j4i
*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 ...##
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Chapter 10: Algebraic Algorithms
[article]

2013
*
arXiv
*
pre-print

Diaz-Herrera, editors, covers Algebraic

arXiv:1311.3731v1
fatcat:whtgwztbmbgqbl44s4e663oulu
*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] . ...##
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Formalizing the LLL Basis Reduction Algorithm and the LLL Factorization Algorithm in Isabelle/HOL

2020
*
Journal of automated reasoning
*

The LLL basis

doi:10.1007/s10817-020-09552-1
pmid:32831440
pmcid:PMC7413592
fatcat:fhfgozhs5zhvzg7zfooxpdiina
*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. ...##
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A Formalization of the LLL Basis Reduction Algorithm
[chapter]

2018
*
Lecture Notes in Computer Science
*

The LLL basis

doi:10.1007/978-3-319-94821-8_10
fatcat:fpazlnxfyrhvzltnl23t6u36e4
*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. ...##
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Decidability of the Membership Problem for 2 × 2 integer matrices

2017
*
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
*

Our

doi:10.1137/1.9781611974782.12
dblp:conf/soda/PotapovS17
fatcat:ghupg4wybvczzdy3stp53bgeni
*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. ...##
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On finding small solutions of modular multivariate polynomial equations
[chapter]

1998
*
Lecture Notes in Computer Science
*

This

doi:10.1007/bfb0054124
fatcat:brktftrufnhebd2gxwy6n4ev2i
*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. ...##
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Computer Algebra Algorithms

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. ...

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

2019
*
arXiv
*
pre-print

Using large copper clusters in

arXiv:1812.05264v3
fatcat:bqdzj255mraepedmwozva2lzze
*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 . ...
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