Drinfeld modules with complex multiplication, Hasse invariants and factoring polynomials over finite fields
نویسندگان
چکیده
منابع مشابه
Drinfeld Modules with Complex Multiplication, Hasse Invariants and Factoring Polynomials over Finite Fields
We present a novel randomized algorithm to factor polynomials over a finite field Fq of odd characteristic using rank 2 Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial f ∈ Fq[x] to be factored) with respect to a random Drinfeld module φ with complex multiplication. Factors of f supported on prime ideals with supersin...
متن کاملFactoring Polynomials over Finite Fields using Drinfeld Modules with Complex Multiplication
We present novel algorithms to factor polynomials over a finite field Fq of odd characteristic using rank 2 Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial f(x) ∈ Fq[x] to be factored) with respect to a Drinfeld module φ with complex multiplication. Factors of f(x) supported on prime ideals with supersingular reducti...
متن کاملAddendum to "Factoring polynomials over finite fields with Drinfeld modules"
After my paper [2] was electronically published by Mathematics of Computation, I came across the PhD thesis of professor I. Y. Potemine [6]. In Section 4.3 of his thesis, an algorithm for factoring polynomials is proposed which is equivalent to the algorithm discussed in my paper. Potemine’s algorithm is acknowledged in my PhD thesis [1]. Our algorithms were found independently, both as analogu...
متن کاملFactoring polynomials over finite fields with Drinfeld modules
In the following, we describe a way of factoring polynomials in Fq[X] with Drinfeld modules. We furthermore analyse the complexity of the algorithm and compare it to the well-known Cantor-Zassenhaus algorithm. 1. Defining Fq[X ]-module structures with Drinfeld modules Throughout this paper we will denote A = Fq[X ], where q is a power of some prime p, and N ∈ A for the polynomial which is to be...
متن کاملlsogenies of Drinfeld Modules over Finite Fields
K: a global function field of characteristicp # 0 E a fixed algebraic closure of K 00: a distinguished place of K A: the ring of functions in K regular away from cx> F,: a finite field which is an A-algebra VI the A-characteristic of F, (this means that the prime ideal pt, of v is the kernel of the structure morphism A + F4) 4 : a Drinfeld A-module over F, of rank d 7~: The Frobenius endomorphi...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2021
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2020.06.007