An Implementation of the General Number Field Sieve
نویسندگان
چکیده
It was shown in 2] that under reasonable assumptions the general number eld sieve (GNFS) is the asymptotically fastest known factoring algorithm. It is, however, not known how this algorithm behaves in practice. In this report we describe practical experience with our implementation of the GNFS whose rst version was completed in January 1993 at the
منابع مشابه
The Sieve Re-Imagined: Integer Factorization Methods
In this paper, I explain the Quadratic Sieve, its Multiple Polynomial variation, the Number Field Sieve, and give some worked examples of the afore-mentioned algorithms. Using my own Maple implementation of the Quadratic Sieve, I explore the effect of altering one of the parameters of the Quadratic Sieve algorithm, with respect to both time and success rate.
متن کاملAn Implementation of the General Number Field Sieve to Compute Discrete Logarithms mod p
There are many cryptographic protocols the security of which depends on the diiculty of solving the discrete logarithm problem (8], 9], 14], etc.). In 10] and 18] it was described how to apply the number eld sieve algorithm to the discrete logarithm problem in prime elds. This resulted in the asymptotically fastest known discrete log algorithm for nite elds of p elements. Very little is known a...
متن کاملCollecting relations for the Number Field Sieve in GF(p6)
In order to assess the security of cryptosystems based on the discrete logarithm problem in non-prime finite fields, as are the torus-based or pairing-based ones, we investigate thoroughly the case in Fp6 with the Number Field Sieve. We provide new insights, improvements, and comparisons between different methods to select polynomials intended for a sieve in dimension 3 using a special-q strate...
متن کاملCollecting relations for the Number Field Sieve in GF ppq
In order to assess the security of cryptosystems based on the discrete logarithm problem in non-prime finite fields, as are the torus-based or pairing-based ones, we investigate thoroughly the case in Fp6 with the Number Field Sieve. We provide new insights, improvements, and comparisons between different methods to select polynomials intended for a sieve in dimension 3 using a special-q strate...
متن کاملذخیره 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 1993