Fast Primality Proving on Cullen Numbers

نویسنده

  • Tsz-Wo Sze
چکیده

We present a unconditional deterministic primality proving algorithm for Cullen numbers. The expected running time and the worst case running time of the algorithm are Õ(logN) bit operations and Õ(logN) bit operations, respectively.

برای دانلود رایگان 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

Implementing the Asymptotically Fast Version of the Elliptic Curve Primality Proving Algorithm Less Prelimimary Version 040825

The elliptic curve primality proving algorithm is one of the fastest practical algorithms for proving the primality of large numbers. Its running time cannot be proven rigorously, but heuristic arguments show that it should run in time Õ((logN)) to prove the primality of N . An asymptotically fast version of it, attributed to J. O. Shallit, runs in time Õ((logN)). The aim of this article is to ...

متن کامل

Implementing the asymptotically fast version of the elliptic curve primality proving algorithm

The elliptic curve primality proving (ECPP) algorithm is one of the current fastest practical algorithms for proving the primality of large numbers. Its running time currently cannot be proven rigorously, but heuristic arguments show that it should run in time Õ((logN)5) to prove the primality of N . An asymptotically fast version of it, attributed to J. O. Shallit, is expected to run in time Õ...

متن کامل

AN Õ(log(N)) TIME PRIMALITY TEST FOR GENERALIZED CULLEN NUMBERS

Generalized Cullen Numbers are positive integers of the form Cb(n) := nb n + 1. In this work we generalize some known divisibility properties of Cullen Numbers and present two primality tests for this family of integers. The first test is based in the following property of primes from this family: nb n ≡ (−1)b (mod nbn +1). It is stronger and has less computational cost than Fermat’s test (to b...

متن کامل

An Õ(log2(N)) time primality test for generalized Cullen numbers

Generalized Cullen Numbers are positive integers of the form Cb(n) := nb n + 1. In this work we generalize some known divisibility properties of Cullen Numbers and present two primality tests for this family of integers. The first test is based in the following property of primes from this family: nb n ≡ (−1)b (mod nbn +1). It is stronger and has less computational cost than Fermat’s test (to b...

متن کامل

Primality Proving via One round in Ecpp and One Iteration

On August 2002, Agrawal, Kayal and Saxena announced the first deterministic and polynomial time primality testing algorithm. For an input n, the AKS algorithm runs in heuristic time Õ(log n). Verification takes roughly the same amount of time. On the other hand, the Elliptic Curve Primality Proving algorithm (ECPP) runs in random heuristic time Õ(log n) ( Õ(log n) if the fast multiplication is ...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009