Abstract
RSA is one of the most important public key cryptosystems for information security. The security of RSA depends on Integer factorization problem, it relies on the difficulty of factoring large integers. Much research has gone into problem of factoring a large number. Due to advances in factoring algorithms and advances in computing hardware the size of the number that can be factorized increases exponentially year by year. The General Number Field Sieve algorithm (GNFS) is currently the best known method for factoring large numbers over than 110 digits. In this paper, a parallel GNFS implementation on a BA-cluster is presented. This study begins with a discussion of the serial algorithm in general and covers the five steps of the algorithm. Moreover, this approach discusses the parallel algorithm for the sieving step. The experimental results have shown that the algorithm has achieved a good speedup and can be used for factoring a large integers.
Highlights
Factoring is very important in the field of cryptography, in the RSA cryptosystem
The RSA algorithm [5] is the most popular algorithm in public-key cryptosystems and RSA is used in real world applications such as: internet explorer, email systems, and online banking [12]
The security of RSA algorithm relies on the difficulty of factoring large integers
Summary
The General Number Field Sieve (GNFS) algorithm [1], [2] is derived from the Number Fields Sieve (NFS) algorithm, developed by A. GNFS have five major steps which are described as follows: 1) Step 1: (Polynomial selection) Find a polynomial f : R → R of degree d with integer coefficients as follows:.
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