Computing special powers in finite fields
نویسندگان
چکیده
منابع مشابه
Computing special powers in finite fields
We study exponentiation in nonprime finite fields with very special exponents such as they occur, for example, in inversion, primitivity tests, and polynomial factorization. Our algorithmic approach improves the corresponding exponentiation problem from about quadratic to about linear time.
متن کاملPowers in finite fields
There are lots of results on the “random-like” behaviour of square elements in finite fields. For example, they can be used in combinatorial constructions and algorithms, as their properties somehow “imitate” a random distribution. In this paper we investigate the more general question concerning the behaviour of d-th powers in finite fields (where d is a fixed value). Surprisingly, they are di...
متن کاملFactoring 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 کاملPowers in finite groups
If G is a finitely generated profinite group then the verbal subgroup Gq is open. In a d-generator finite group every product of qth powers is a product of f(d, q) qth powers. 20E20, 20F20.
متن کاملComputing Zeta Functions Over Finite Fields
In this report, we discuss the problem of computing the zeta function of an algebraic variety defined over a finite field, with an emphasis on computing the reduction modulo pm of the zeta function of a hypersurface, where p is the characteristic of the finite field. 1991 Mathematics Subject Classification: 11Y16, 11T99, 14Q15.
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: Mathematics of Computation
سال: 2003
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-03-01599-0