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Parallel Algorithms for Integer Factorisation
"... The problem of finding the prime factors of large composite numbers has always been of mathematical interest. With the advent of public key cryptosystems it is also of practical importance, because the security of some of these cryptosystems, such as the RivestShamirAdelman (RSA) system, depends o ..."
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Cited by 43 (17 self)
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The problem of finding the prime factors of large composite numbers has always been of mathematical interest. With the advent of public key cryptosystems it is also of practical importance, because the security of some of these cryptosystems, such as the RivestShamirAdelman (RSA) system, depends on the difficulty of factoring the public keys. In recent years the best known integer factorisation algorithms have improved greatly, to the point where it is now easy to factor a 60decimal digit number, and possible to factor numbers larger than 120 decimal digits, given the availability of enough computing power. We describe several algorithms, including the elliptic curve method (ECM), and the multiplepolynomial quadratic sieve (MPQS) algorithm, and discuss their parallel implementation. It turns out that some of the algorithms are very well suited to parallel implementation. Doubling the degree of parallelism (i.e. the amount of hardware devoted to the problem) roughly increases the size of a number which can be factored in a fixed time by 3 decimal digits. Some recent computational results are mentioned – for example, the complete factorisation of the 617decimal digit Fermat number F11 = 2211 + 1 which was accomplished using ECM.
Computing Discrete Logarithms with Quadratic Number Rings
 Advances in Cryptology  EUROCRYPT '98, LNCS 1403
, 1998
"... At present, there are two competing index calculus variants for computing discrete logarithms in (Z/pZ) * in practice. The purpose of this paper is to summarize the recent practical experience with a generalized implementation covering both a variant of the Number Field Sieve and the Gaussian intege ..."
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Cited by 7 (1 self)
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At present, there are two competing index calculus variants for computing discrete logarithms in (Z/pZ) * in practice. The purpose of this paper is to summarize the recent practical experience with a generalized implementation covering both a variant of the Number Field Sieve and the Gaussian integer method. By this implementation we set a record with p consisting of 85 decimal digits. With regard to computational results, including the running time, we provide a comparison of the two methods for this value of p.
Application of BioInspired Algorithm to the Problem of Integer Factorisation
 International Journal of BioInspired Computation (IJBIC
"... integer factorisation ..."
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Optimal Parameterization of SNFS
, 2003
"... The Special Number Field Sieve factoring algorithm has a large number of parametric choices, each of which can affect its run time. We give guidelines for these choices along with a discussion of useful coding optimizations. We also give a theoretical argument which proves that the choice of sieving ..."
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Cited by 1 (0 self)
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The Special Number Field Sieve factoring algorithm has a large number of parametric choices, each of which can affect its run time. We give guidelines for these choices along with a discussion of useful coding optimizations. We also give a theoretical argument which proves that the choice of sieving region that has been used so far in successful factorizations is not optimal and show how to obtain an improved sieve region. The improvement has yielded a 15% speed increase in practice.