𝒫-schemes and Deterministic Polynomial Factoring over Finite Fields
نویسنده
چکیده
منابع مشابه
P-schemes: a unifying framework for deterministic polynomial factoring over finite fields
We introduce a family of mathematical objects called P-schemes, generalizing the notions of association schemes andm-schemes [IKS09]. Based on these objects, we develop a unifying framework for deterministic polynomial factoring over finite fields under the generalized Riemann hypothesis (GRH). It allows us to not only recover most of the known results but also discover new ones. In particular,...
متن کامل$\mathcal{P}$-schemes and Deterministic Polynomial Factoring over Finite Fields
We introduce a family of mathematical objects called $\mathcal{P}$-schemes, where $\mathcal{P}$ is a poset of subgroups of a finite group $G$. A $\mathcal{P}$-scheme is a collection of partitions of the right coset spaces $H\backslash G$, indexed by $H\in\mathcal{P}$, that satisfies a list of axioms. These objects generalize the classical notion of association schemes as well as the notion of $...
متن کاملNew Algorithms for Finding Irreducible Polynomials over Finite Fields
We present a new algorithm for finding an irreducible polynomial of specified degree over a finite field. Our algorithm is deterministic, and it runs in polynomial time for fields of small characteristic. We in fact prove the stronger result that the problem of finding irreducible polynomials of specified degree over a finite field is deterministic polynomial-time reducible to the problem of fa...
متن کاملTrading GRH for algebra: algorithms for factoring polynomials and related structures
In this paper we develop techniques that eliminate the need of the Generalized Riemann Hypothesis (GRH) from various (almost all) known results about deterministic polynomial factoring over finite fields. Our main result shows that given a polynomial f(x) of degree n over a finite field k, we can find in deterministic poly(n n, log |k|) time either a nontrivial factor of f(x) or a nontrivial au...
متن کاملOn the Deterministic Complexity of Factoring Polynomials
The paper focuses on the deterministic complexity of factoring polynomials over finite fields assuming the extended Riemann hypothesis (ERH). By the works of Berlekamp (1967, 1970) and Zassenhaus (1969), the general problem reduces deterministically in polynomial time to finding a proper factor of any squarefree and completely splitting polynomial over a prime field Fp . Algorithms are designed...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1706.10028 شماره
صفحات -
تاریخ انتشار 2017