The number field sieve

نویسنده

  • PETER STEVENHAGEN
چکیده

We describe the main ideas underlying integer factorization using the number field sieve.

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

A Description of the Number Field Sieve

The number field sieve is a relatively new method to factor large integers. Its most notable success is the factorization of the ninth Fermat number. It is significantly faster than all known existing integer factoring algorithms. We examine the theoretical underpinnings of the sieve; after understanding how it works, we state the algorithm. We look mostly to the algebraic number theory aspects...

متن کامل

On Class Group Computations Using the Number Field Sieve

The best practical algorithm for class group computations in imaginary quadratic number fields (such as group structure, class number, discrete logarithm computations) is a variant of the quadratic sieve factoring algorithm. Paradoxical as it sounds, the principles of the number field sieve, in a strict sense, could not be applied to number field computations, yet. In this article we give an in...

متن کامل

A construction of 3-dimensional lattice sieve for number field sieve over F_{p^n}

The security of pairing-based cryptography is based on the hardness of solving the discrete logarithm problem (DLP) over extension field GF(p) of characteristic p and degree n. Joux et al. proposed an asymptotically fastest algorithm for solving DLP over GF(p) (JLSV06-NFS) as the extension of the number field sieve over prime field GF(p) (JL03-NFS). The lattice sieve is often used for a largesc...

متن کامل

The Number Field Sieve in the Medium Prime Case

In this paper, we study several variations of the number field sieve to compute discrete logarithms in finite fields of the form Fpn , with p a medium to large prime. We show that when n is not too large, this yields a Lpn(1/3) algorithm with efficiency similar to that of the regular number field sieve over prime fields. This approach complements the recent results of Joux and Lercier on the fu...

متن کامل

Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method

In this paper, we describe many improvements to the number field sieve. Our main contribution consists of a new way to compute individual logarithms with the number field sieve without solving a very large linear system for each logarithm. We show that, with these improvements, the number field sieve outperforms the gaussian integer method in the hundred digit range. We also illustrate our resu...

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 2005