Factoring Polynomials over Special Finite Fields
نویسندگان
چکیده
منابع مشابه
Factoring Polynomials over Special Finite Fields
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...
متن کاملFactoring Dickson polynomials over finite fields
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.
متن کاملSmoothness and Factoring Polynomials Over Finite Fields
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...
متن کاملFactoring Polynomials Over Finite Fields: A Survey
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...
متن کاملFactoring Multivariate Polynomials over Finite Fields
We consider the deterministic complexity of the problem of polynomial factorization over finite fields given a finite field Fq and a polynomial h(x, y) ∈ Fq[x, y] compute the unique factorization of h(x, y) as a product of irreducible polynomials. This problem admits a randomized polynomial-time algorithm and no deterministic polynomial-time algorithm is known. In this chapter, we give a determ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2001
ISSN: 1071-5797
DOI: 10.1006/ffta.2000.0306