Factoring Polynomials Over Large Finite Fields
نویسندگان
چکیده
منابع مشابه
Factoring Multivariate Polynomials over Large Finite Fields
A simple probabilistic algorithm is presented to find the irreducible factors of a bivariate polynomial over a large finite field. For a polynomial f(x, y) over F of total degree n , our algorithm takes at most 4.89, 2 , n log n log q operations in F to factor f(x , y) completely. This improves a probabilistic factorization algorithm of von zur Gathen and Kaltofen, which takes 0(n log n log q) ...
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We derive the factorizations of the Dickson polynomials Dn(X, a) and En(X, a), and of the bivariate Dickson polynomials Dn(X, a) − Dn(Y, a), over any finite field. Our proofs are significantly shorter and more elementary than those previously known.
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Let p be a prime number, and F p the nite eld with p elements. Let S(m) be the \smoothness" function that for integers m is deened as the largest prime divisor of m. In this note, we prove the following theorem. Theorem. There is a deterministic algorithm for factoring polynomials over F p , which on poly-nomials over F p of degree n runs in time S(p ? 1) 1=2 (n log p) O(1) under the assumption...
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We exhibit a deterministic algorithm for factoring polynomials in one variable over "nite "elds. It is e$cient only if a positive integer k is known for which ' k (p) is built up from small prime factors; here ' k denotes the kth cyclotomic polynomial, and p is the characteristic of the "eld. In the case k"1, when ' k (p)"p!1, such an algorithm was known, and its analysis required the generaliz...
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Finding the factorization of a polynomial over a finite field is of interest not only independently but also for many applications in computer algebra, algebraic coding theory, cryptography, and computational number theory. Polynomial factorization over finite fields is used as a subproblem in algorithms for factoring polynomials over the integers (Zassenhaus, 1969; Collins, 1979; Lenstra et al...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1970
ISSN: 0025-5718
DOI: 10.2307/2004849