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How to break Gifford's cipher (extended abstract)

1994
*
Proceedings of the 2nd ACM Conference on Computer and communications security - CCS '94
*

We present.

doi:10.1145/191177.191227
dblp:conf/ccs/CainS94
fatcat:lcpp32olazdjnl4av62jxxvo2i
*and*implement a ,ciphertext-only algorithm to break Gifford's cipher, a stream cipher designed in 1984 by David Gifford*of*MIT*and*used to encrypt New York Times*and*Associated Press wire reports ... Applying linear algebra over finite fields, we exploit a time-space tradeoff to separately determine key segments derived from a decomposition*of*the feedback function. ... Rueppel,*and*Richard Stein for editorial comments. All computer work was carried out on workstations at the University*of*Maryland Baltimore County. ...##
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Efficient Decomposition of Bimatrix Games (Extended Abstract)

2014
*
Electronic Proceedings in Theoretical Computer Science
*

The algorithm is fixed-parameter tractable with the size

doi:10.4204/eptcs.146.10
fatcat:iy6bjjsmmjgj7hdtqjgahd65pm
*of*the largest*irreducible*component*of*a game as parameter. ... Exploiting the algebraic structure*of*the set*of*bimatrix games, a divide-*and*-conquer algorithm for finding Nash equilibria is proposed. ... One comment in particular was instrumental in improving the runtime analysis*of*our algorithm to a quadratic exponent. ...##
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Checking the convexity of polytopes and the planarity of subdivisions (extended abstract)
[chapter]

1997
*
Lecture Notes in Computer Science
*

In particular, we design simple optimal checkers for convex polytopes in two

doi:10.1007/3-540-63307-3_59
fatcat:lbpnbl3qbjefbgq7uyuvwx2wai
*and*higher dimensions,*and*for various types*of*planar subdivisions, such as triangulations, Delaunay triangulations,*and*convex ... This paper considers the problem*of*verifying the correctness*of*geometric structures. ... Acknowledgments We w ould like to thank Giuseppe Di Battista, Michael Goodrich, David Kirkpatrick,*and*Luca Vismara for useful discussions. ...##
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Theoretical Properties
[chapter]

2015
*
The Fence Methods
*

There exists at most one full

doi:10.1142/9789814596077_0009
fatcat:7rmqxc74afagha2moms4jjz35u
*factorization**of*f which*extends*the boundary*factorization*defined by the given (g γ ) γ∈Γ*and*(h γ ) γ∈Γ . ... Contents In this section we*extend*the univariate*factorization*techniques*of*the previous section to several variables. ... Minkowski sum, 9 Newton polytope, 9 NP-hardness, 11 Ostrowski theorem, 9 separable*factorization*, 3 sparse*factorization*, 9 sparse*polynomial*representation, 9 straight-line program, 11, 12 straight-line ...##
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Theoretical Properties
[chapter]

2011
*
Chapman & Hall/CRC Biostatistics Series
*

There exists at most one full

doi:10.1201/b10783-7
fatcat:zqyyjtuzsjf7zpekrozupsqwye
*factorization**of*f which*extends*the boundary*factorization*defined by the given (g γ ) γ∈Γ*and*(h γ ) γ∈Γ . ... Contents In this section we*extend*the univariate*factorization*techniques*of*the previous section to several variables. ... Minkowski sum, 9 Newton polytope, 9 NP-hardness, 11 Ostrowski theorem, 9 separable*factorization*, 3 sparse*factorization*, 9 sparse*polynomial*representation, 9 straight-line program, 11, 12 straight-line ...##
###
Theoretical Properties
[chapter]

2013
*
Handbook of Finite Fields
*

There exists at most one full

doi:10.1201/b15006-5
fatcat:cubpnr7y3fbfpivjinvw2dqmvy
*factorization**of*f which*extends*the boundary*factorization*defined by the given (g γ ) γ∈Γ*and*(h γ ) γ∈Γ . ... Contents In this section we*extend*the univariate*factorization*techniques*of*the previous section to several variables. ... Minkowski sum, 9 Newton polytope, 9 NP-hardness, 11 Ostrowski theorem, 9 separable*factorization*, 3 sparse*factorization*, 9 sparse*polynomial*representation, 9 straight-line program, 11, 12 straight-line ...##
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Effective Noether irreducibility forms and applications

1991
*
Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91
*

the complex

doi:10.1145/103418.103431
dblp:conf/stoc/Kaltofen91
fatcat:3gg6qt7nobfbta4jzjoyvqqoqm
*factors**of*a multivariate integral*polynomial*,*and*how to count the number*of*absolutely*irreducible**factors**of*a multivariate*polynomial*with coefficients in a rational function field, both ... A specific*polynomial**of*a certain degree is absolutely*irreducible*, if*and*only if all the corresponding*irreducibility*forms vanish when evaluated at the coefficients*of*the specific*polynomial*. ... The development*of**polynomial*-time multivariate*polynomial**factorization*algorithms has lead to new approaches for absolute*irreducibility**testing**and**factorization*(Heintz*and*Sieveking 1981) , (Davenport ...##
###
Effective Noether Irreducibility Forms and Applications

1995
*
Journal of computer and system sciences (Print)
*

the complex

doi:10.1006/jcss.1995.1023
fatcat:xkaq7zcrujdpthdjwczoionsci
*factors**of*a multivariate integral*polynomial*,*and*how to count the number*of*absolutely*irreducible**factors**of*a multivariate*polynomial*with coefficients in a rational function field, both ... A specific*polynomial**of*a certain degree is absolutely*irreducible*, if*and*only if all the corresponding*irreducibility*forms vanish when evaluated at the coefficients*of*the specific*polynomial*. ... The development*of**polynomial*-time multivariate*polynomial**factorization*algorithms has lead to new approaches for absolute*irreducibility**testing**and**factorization*(Heintz*and*Sieveking 1981) , (Davenport ...##
###
Page 3428 of Mathematical Reviews Vol. , Issue 86h
[page]

1986
*
Mathematical Reviews
*

In this paper an algorithm is presented which determines the number

*of**factors**of*a*polynomial*in*polynomial*time. ... J. (1-BELL) Finding the number*of**factors**of*a*polynomial*. J. Algorithms 5 (1984), no. 2, 180-186. ...##
###
Page 3994 of Mathematical Reviews Vol. , Issue 84j
[page]

1984
*
Mathematical Reviews
*

Let K denote a fixed

*polynomial*in GF{q, x]. Then 21/|P| converges, where the sum*extends*over all “primary” (monic)*irreducible**polynomials*P for which P+ K is also*irreducible*. ... The computational requirements are compared with a related*test*for maximum length*and*also with some common*factorization*procedures. ...##
###
The Numerical Factorization of Polynomials

2015
*
Foundations of Computational Mathematics
*

As a regularization, this paper formulates the notion

doi:10.1007/s10208-015-9289-1
fatcat:dxhaewoqjffbrp3occhjgxzrui
*of*numerical*factorization*based on the geometry*of**polynomial*spaces*and*the stratification*of**factorization*manifolds. ... robust*and*efficient algorithm with a MATLAB implementation capable*of*accurate*polynomial**factorizations*using floating point arithmetic even if the coefficients are perturbed. ... Then there is an*irreducible**polynomial*f*of*degree m*and*a sequence*of**factorable**polynomials*{ p j } ∞ j=1 approaching f . ...##
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Towards toric absolute factorization

2009
*
Journal of symbolic computation
*

This article presents an algorithmic approach to study

doi:10.1016/j.jsc.2008.03.007
fatcat:mtvedlfcrbgyxa5xxrz3zegx34
*and*compute the absolute*factorization**of*a bivariate*polynomial*, taking into account the geometry*of*its monomials. ... It is based on algebraic criterions inherited from algebraic interpolation*and*toric geometry. ...*Abstract*toric surfaces Let Q ⊂ R 2 be a two-dimensional integer convex polytope satisfying the condition*of*Lemma 6. ...##
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Extended Period LFSR Using Variable TAP Function

2008
*
18th International Conference on Electronics, Communications and Computers (conielecomp 2008)
*

This paper presents a method to

doi:10.1109/conielecomp.2008.8
dblp:conf/conielecomp/Molina-RuedaUU08
fatcat:y3kl6pvplfhuvmx3jhxwfvrqoy
*extend*the period*of*a Linear Feedback Shift Register (LFSR) by proposing an algorithm to generate primitive*polynomials*, this is archived by using basic LFSR with a maximum ... Also by separating the phases*of*setup*and*running in the algorithm avoid losing the characteristically speed*of*the LFSRs. ...*EXTENDING*THE PERIOD TO THE MAXIMUM The extension*of*the period is calculated by: I(2 127 − 1) Where I is the total number*of*existing*irreducible**polynomials*which according to Sloane's series A011260 ...##
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ElGamal Public-Key cryptosystem in multiplicative groups of quotient rings of polynomials over finite fields

2005
*
Computer Science and Information Systems
*

The later requires finding

doi:10.2298/csis0501063e
fatcat:ham57rbwvvd6hfuo33h6hgndrm
*irreducible**polynomials*h(x)*and*constructing the quotient ring . El-Kassar et al. modified the ElGamal scheme to the domain*of*Gaussian integers. ... In this paper, we consider another extension employing the group*of*units*of*, where is a product*of**irreducible**polynomials*whose degrees are pairwise relatively prime. ... There is an efficient algorithm for*testing*whether or not f(x) is a primitive*polynomial*whenever the*factorization**of*the integer 2 d −1 is known. ...##
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Combinatorial Resultants in the Algebraic Rigidity Matroid
[article]

2021
*
arXiv
*
pre-print

Our algorithm performs an algebraic elimination guided by the construction tree,

arXiv:2103.08432v1
fatcat:psdqebn445bwfdsx3tqf7ovute
*and*uses classical resultants,*factorization**and*ideal membership. ... We introduce combinatorial resultants, a new operation on graphs that captures properties*of*the Sylvester resultant*of*two*polynomials*in the algebraic rigidity matroid. ... A*polynomial**factorization**and*a*test**of*membership in the ideal is applied to identify the*factor*which is the circuit*polynomial*. ...
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