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4,518
Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 961 (11 self)
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In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive
Random Polynomials and Polynomial Factorization
 TO APPEAR IN AUTOMATA, LANGUAGES AND PROGRAMMING, PROCEEDINGS OF THE 23RD ICALP COLLOQUIUM, PADERBORN, JULY 1996, F. MEYER AUF DER HEIDE, ED.
, 1996
"... We give a precise averagecase analysis of a complete polynomial factorization chain over finite fields by methods based on generating functions and singularity analysis. ..."
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Cited by 10 (3 self)
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We give a precise averagecase analysis of a complete polynomial factorization chain over finite fields by methods based on generating functions and singularity analysis.
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 1277 (4 self)
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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration
A NEW POLYNOMIALTIME ALGORITHM FOR LINEAR PROGRAMMING
 COMBINATORICA
, 1984
"... We present a new polynomialtime algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than the ell ..."
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Cited by 860 (3 self)
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We present a new polynomialtime algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than
Schemes for Deterministic Polynomial Factoring
, 2008
"... In this work we relate the deterministic complexity of factoring polynomials (over finite fields) to certain combinatorial objects we call mschemes. We extend the known conditional deterministic subexponential time polynomial factoring algorithm for finite fields to get an underlying mscheme. We d ..."
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Cited by 4 (1 self)
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In this work we relate the deterministic complexity of factoring polynomials (over finite fields) to certain combinatorial objects we call mschemes. We extend the known conditional deterministic subexponential time polynomial factoring algorithm for finite fields to get an underlying mscheme. We
Multivariate Polynomial Factorization
 J. ACM
, 1973
"... algorithms ........................................... 21 7. Squarefree factorization ...................................... 24 8. Hnsel constructions .......................................... 27 a. Solution of a polynomial equation ......................... 27 b. Linear Hensel construction ....... ..."
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Cited by 25 (0 self)
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algorithms ........................................... 21 7. Squarefree factorization ...................................... 24 8. Hnsel constructions .......................................... 27 a. Solution of a polynomial equation ......................... 27 b. Linear Hensel construction
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factol: It is not clear whether this is still true when quantum mechanics is taken into consider ..."
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Cited by 1111 (5 self)
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of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored. These two problems are generally considered hard on a classical computer and have been used as the basis of several proposed cryptosystems. (We thus give the first examples of quantum cryptanulysis.)
Why the characteristic polynomial factors
 BULL. AMER. MATH. SOC
, 1999
"... We survey three methods for proving that the characteristic polynomial of a finite ranked lattice factors over the nonnegative integers and indicate how they have evolved recently. The first technique uses geometric ideas and is based on Zaslavsky’s theory of signed graphs. The second approach is a ..."
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Cited by 20 (2 self)
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We survey three methods for proving that the characteristic polynomial of a finite ranked lattice factors over the nonnegative integers and indicate how they have evolved recently. The first technique uses geometric ideas and is based on Zaslavsky’s theory of signed graphs. The second approach
Polynomial Factorization Challenges
 List of papers published in the Reports on Computer Algebra series
, 1996
"... Joachim von zur Gathen has proposed a challenge for factoring univariate polynomials over finite fields to evaluate the practicability of current factorization algorithms ("A Factorization Challenge", SIGSAM Bulletin 26(2):2224, 1992). More recently, Victor Shoup has proposed an alternate ..."
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Cited by 3 (0 self)
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Joachim von zur Gathen has proposed a challenge for factoring univariate polynomials over finite fields to evaluate the practicability of current factorization algorithms ("A Factorization Challenge", SIGSAM Bulletin 26(2):2224, 1992). More recently, Victor Shoup has proposed
Results 1  10
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4,518