Factoring Polynominals over p-Adic Fields

نویسندگان

  • David G. Cantor
  • Daniel M. Gordon
چکیده

We give an efficient algorithm for factoring polynomials over finite algebraic extensions of the p-adic numbers. This algorithm uses ideas of Chistov’s random polynomial-time algorithm, and is suitable for practical implementation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Factoring polynomials over p-adic elds

We give an eecient algorithm for factoring polynomials over nite algebraic extensions of the p-adic numbers. This algorithm uses ideas of Chistov's random polynomial-time algorithm, and is suitable for practical implementation.

متن کامل

Computing automorphisms of abelian number fields

Let L = Q(α) be an abelian number field of degree n. Most algorithms for computing the lattice of subfields of L require the computation of all the conjugates of α. This is usually achieved by factoring the minimal polynomial mα(x) of α over L. In practice, the existing algorithms for factoring polynomials over algebraic number fields can handle only problems of moderate size. In this paper we ...

متن کامل

Algebraic Number Theory Notes

1. Unique Prime Factorization of Ideals: 21 September 2010 2 2. Minkowski Theory: 28 September 2010 5 October 2010 4 3. Cyclotomic Fields and Fermat: 6 13 October 2010 9 4. Multiplicative Minkowski and Dirichlet’s Unit Theorem: 19 26 October 2010 10 5. Factoring Rational Primes in Algebraic Number Fields: 26 October 2010 14 6. Application to Zeta Functions: 3 9 November 2010 18 7. Hilbert’s Ram...

متن کامل

Pro-p hom-form of the birational anabelian conjecture over sub-p-adic fields

We prove a Hom-form of the pro-p birational anabelian conjecture for function fields over sub-p-adic fields. Our starting point is the corresponding Theorem of Mochizuki in the case of transcendence degree 1.

متن کامل

A p-adic Height Function Of Cryptanalytic Significance

It is noted that an efficient algorithm for calculating a p-adic height could have cryptanalytic applications. Elliptic curves and their generalizations are an active research topic with practical applications in cryptography [1], [2], [3]. If E is an elliptic curve defined over a finite field Fp, where p is prime, and if P and Q are points on the curve E such that Q = nP , then the elliptic cu...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000