منابع مشابه
A General Polynomial Sieve
An important component of the index calculus methods for finding discrete logarithms is the acquisition of smooth polynomial relations. Gordon and McCurley (1992) developed a sieve to aid in finding smooth Coppersmith polynomials for use in the index calculus method. We discuss their approach and some of the difficulties they found with their sieve. We present a new sieving method that can be a...
متن کاملAn Introduction to the General Number Field Sieve
With the proliferation of computers into homes and businesses and the explosive growth rate of the Internet, the ability to conduct secure electronic communications and transactions has become an issue of vital concern. One of the most prominent systems for securing electronic information, known as RSA, relies upon the fact that it is computationally difficult to factor a " large " integer into...
متن کاملAn Implementation of the General Number Field Sieve
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
متن کاملOn polynomial selection for the general number field sieve
The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records. 1. The polynomial selection method of Montgomery and Murphy In this section we brief...
متن کاملA Beginner’s Guide To The General Number Field Sieve
RSA is a very popular public key cryptosystem. This algorithm is known to be secure, but this fact relies on the difficulty of factoring large numbers. Because of the popularity of the algorithm, much research has gone into this problem of factoring a large number. The size of the number that we are able to factor increases exponentially year by year. This fact is partly due to advancements in ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1964
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-10-1-31-62