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How to break Gifford's cipher (extended abstract)

Thomas R. Cain, Alan T. Sherman
1994 Proceedings of the 2nd ACM Conference on Computer and communications security - CCS '94  
We present. 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.  ... 
doi:10.1145/191177.191227 dblp:conf/ccs/CainS94 fatcat:lcpp32olazdjnl4av62jxxvo2i

Efficient Decomposition of Bimatrix Games (Extended Abstract)

Xiang Jiang, Arno Pauly
2014 Electronic Proceedings in Theoretical Computer Science  
The algorithm is fixed-parameter tractable with the size 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.  ... 
doi:10.4204/eptcs.146.10 fatcat:iy6bjjsmmjgj7hdtqjgahd65pm

Checking the convexity of polytopes and the planarity of subdivisions (extended abstract) [chapter]

O. Devillers, G. Liotta, F. P. Preparata, R. Tamassia
1997 Lecture Notes in Computer Science  
In particular, we design simple optimal checkers for convex polytopes in two 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.  ... 
doi:10.1007/3-540-63307-3_59 fatcat:lbpnbl3qbjefbgq7uyuvwx2wai

Theoretical Properties [chapter]

2015 The Fence Methods  
There exists at most one full 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  ... 
doi:10.1142/9789814596077_0009 fatcat:7rmqxc74afagha2moms4jjz35u

Theoretical Properties [chapter]

2011 Chapman & Hall/CRC Biostatistics Series  
There exists at most one full 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  ... 
doi:10.1201/b10783-7 fatcat:zqyyjtuzsjf7zpekrozupsqwye

Theoretical Properties [chapter]

2013 Handbook of Finite Fields  
There exists at most one full 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  ... 
doi:10.1201/b15006-5 fatcat:cubpnr7y3fbfpivjinvw2dqmvy

Effective Noether irreducibility forms and applications

Erich Kaltofen
1991 Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91  
the complex 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  ... 
doi:10.1145/103418.103431 dblp:conf/stoc/Kaltofen91 fatcat:3gg6qt7nobfbta4jzjoyvqqoqm

Effective Noether Irreducibility Forms and Applications

E. Kaltofen
1995 Journal of computer and system sciences (Print)  
the complex 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  ... 
doi:10.1006/jcss.1995.1023 fatcat:xkaq7zcrujdpthdjwczoionsci

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

Wenyuan Wu, Zhonggang Zeng
2015 Foundations of Computational Mathematics  
As a regularization, this paper formulates the notion 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 .  ... 
doi:10.1007/s10208-015-9289-1 fatcat:dxhaewoqjffbrp3occhjgxzrui

Towards toric absolute factorization

M. Elkadi, A. Galligo, M. Weimann
2009 Journal of symbolic computation  
This article presents an algorithmic approach to study 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.  ... 
doi:10.1016/j.jsc.2008.03.007 fatcat:mtvedlfcrbgyxa5xxrz3zegx34

Extended Period LFSR Using Variable TAP Function

Ariel Molina-Rueda, Fernando Uceda-Ponga, Claudia Feregrino Uribe
2008 18th International Conference on Electronics, Communications and Computers (conielecomp 2008)  
This paper presents a method to 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  ... 
doi:10.1109/conielecomp.2008.8 dblp:conf/conielecomp/Molina-RuedaUU08 fatcat:y3kl6pvplfhuvmx3jhxwfvrqoy

ElGamal Public-Key cryptosystem in multiplicative groups of quotient rings of polynomials over finite fields

A.N. El-Kassar, Ramzi Haraty
2005 Computer Science and Information Systems  
The later requires finding 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.  ... 
doi:10.2298/csis0501063e fatcat:ham57rbwvvd6hfuo33h6hgndrm

Combinatorial Resultants in the Algebraic Rigidity Matroid [article]

Goran Malić, Ileana Streinu
2021 arXiv   pre-print
Our algorithm performs an algebraic elimination guided by the construction tree, 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.  ... 
arXiv:2103.08432v1 fatcat:psdqebn445bwfdsx3tqf7ovute
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