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The Quadratic Sieve Factoring Algorithm
, 2001
"... Mathematicians have been attempting to find better and faster ways to factor composite numbers since the beginning of time. Initially this involved dividing a number by larger and larger primes until you had the factorization. This trial division was not improved upon until Fermat applied the ..."
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Mathematicians have been attempting to find better and faster ways to factor composite numbers since the beginning of time. Initially this involved dividing a number by larger and larger primes until you had the factorization. This trial division was not improved upon until Fermat applied the
THE NUMBER FIELD SIEVE FACTORING ALGORITHM
"... In my last paper, I described the Quadratic Sieve (QS) and it’s variants, including a very abbreviated history of the factoring problem. In this paper I will discuss the Number Field Sieve (NFS), that is, the algorithm itself, along with several variants, and how it applies to ..."
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In my last paper, I described the Quadratic Sieve (QS) and it’s variants, including a very abbreviated history of the factoring problem. In this paper I will discuss the Number Field Sieve (NFS), that is, the algorithm itself, along with several variants, and how it applies to
A Study on Parallel RSA Factorization
"... Abstract—The RSA cryptosystem is one of the widely used public key systems. The security of it is based on the intractability of factoring a large composite integer into two component primes, which is referred to as the RSA assumption. So far, the Quadratic Sieve (QS) is the fastest and generalpurp ..."
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Abstract—The RSA cryptosystem is one of the widely used public key systems. The security of it is based on the intractability of factoring a large composite integer into two component primes, which is referred to as the RSA assumption. So far, the Quadratic Sieve (QS) is the fastest and generalpurpose method for factoring composite numbers having less than about 110 digits. In this paper, we present our study on a variant of the QS, i.e., the Multiple Polynomial Quadratic Sieve (MPQS) for simulating the parallel RSA factorization. The parameters of our enhanced methods (such as the size of the factor base and the length of the sieving interval) are benefit to reduce the overall running time and the computation complexity is actually lower. The experimental result shows that it only takes 6.6 days for factoring larger numbers of 100 digits using the enhanced MPQS by 32 workstations.