Factorization of RSA-140 using the number field sieve

On February 2, 1999, we completed the factorization of the 140-digit number RSA-140 with the help of the Number Field Sieve factoring method (NFS). This is a new general factoring record. The previous record was established on April 10, 1996 by the factorization of the 130-digit number RSA-130, also with the help of NFS. The amount of computing time spent on RSA-140 was roughly twice that needed for RSA-130, about half of what could be expected from a straightforward extrapolation of the computing time spent on factoring RSA-130. The speed-up can be attributed to a new polynomial selection method for NFS which will be sketched in this paper

Be our guest/worker: reciprocal dependency and expressions of hospitality in Ni-Vanuatu overseas labour migration

Whilst there has been renewed interest in the development potential of temporary migration programmes, such schemes have long been criticized for creating conditions for exploitation and fostering dependence. In this article, which is based on a case study of Ni-Vanuatu seasonal workers employed in New Zealand’s horticultural industry, I show how workers and employers alike actively cultivate and maintain relations of reciprocal dependence and often describe their relation in familial terms of kinship and hospitality. Nevertheless, workers often feel estranged both in the Marxian sense of being subordinated to a regime of time-discipline, and in the intersubjective sense of feeling disrespected or treated unkindly. I show how attention to the ‘non-contractual element’ in the work contract, including expressions of hospitality, can contribute to anthropological debates surrounding work, migration, and dependence, and to interdisciplinary understandings of the justice of labour migration.ESRC scholarship (project reference ES/H034943/1

Factorization of a 512 bit RSA modulus

This paper reports on the factorization of the 512 bit number RSA-155 by the number field Sieve factoring method (NFS) and discusses the implications for RS

The three-large-primes variant of the number field sieve

The Number Field Sieve (NFS) is the asymptotically fastest known factoringalgorithm for large integers.This method was proposed by John Pollard in 1988. Sincethen several variants have been implemented with the objective of improving thesiever which is the most time consuming part of this method (but fortunately,also the easiest to parallelise).Pollard's original method allowed one large prime. After that thetwo-large-primes variant led to substantial improvements.In this paperwe investigate whether the three-large-primes variant may lead to any furtherimprovement. We present theoretical expectations and experimental results.We assume the reader to be familiar with the NFS.As a side-result, we improved some formulae for Taylor coefficients ofDickman's $ho$ function given by Patterson and Rumsey andMarsaglia, Zaman and Marsaglia

MPQS with three large primes

We report the factorization of a 135-digit integer by the triple-large-prime variation of the multiple polynomial quadratic sieve. Previous workers [6][10] had suggested that using more than two large primes would be counterproductive, because of the greatly increased number of false reports from the sievers. We provide evidence that, for this number and our implementation, using three large primes is approximately 1.7 times as fast as using only two. The gain in efficiency comes from a sudden growth in the number of cycles arising from relations which contain three large primes. This effect, which more than compensates for the false reports, was not anticipated by the authors of [6] [10] but has become quite familiar from factorizations obtained using the number field sieve. We characterize the various types of cycles present, and give a semi-quantitative description of their rather mysterious behaviour

A kilobit special number field sieve factorization

We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 2 1039 − 1. Although this factorization is orders of magnitude ‘easier ’ than a factorization of a 1024-bit RSA modulus is believed to be, the methods we used to obtain our result shed new light on the feasibility of the latter computation