The paper focuses on the deterministic complexity of factoring polynomials over finite fields assuming the extended Riemann hypothesis (ERH). By the works of and , the general problem reduces deterministically in polynomial time to finding a proper factor of any squarefree and completely splitting
On the deterministic complexity of factoring polynomials over finite fields
β Scribed by Victor Shoup
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 792 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0020-0190
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π SIMILAR VOLUMES
We analyze the problem of finding the roots of an arbitrary polynomial over a finite field (equivalent to factoring an arbitrary polynomial over the field) and propose a deterministic approach which leads to a combinatorial problem whose satisfactory solution would yield a factoring method which is
Let T n (x, a) Κ¦ GF(q)[x] be a Dickson polynomial over the finite field GF(q) of either the first kind or the second kind of degree n in the indeterminate x and with parameter a. We give a complete description of the factorization of T n (x, a) over GF(q).
Counting irreducible factors of polynomials over a finite field, Discrete Mathematics, 112 (1993) 103-l 18. Let F,[X] denote a polynomial ring in an indeterminate X over a finite field IF,. Exact formulae are derived for (i) the number of polynomials of degree n in F,[X] with a specified number of i