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On the factorization of RSA120
, 1994
"... We present data concerning the factorization of the 120digit number RSA120, which we factored on July 9, 1993, using the quadratic sieve method. The factorization took approximately 825 MIPS years and was completed within three months real time. At the time of writing RSA120 is the largest inte ..."
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Cited by 15 (3 self)
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We present data concerning the factorization of the 120digit number RSA120, which we factored on July 9, 1993, using the quadratic sieve method. The factorization took approximately 825 MIPS years and was completed within three months real time. At the time of writing RSA120 is the largest integer ever factored by a general purpose factoring algorithm. We also present some conservative extrapolations to estimate the difficulty of factoring even larger numbers, using either the quadratic sieve method or the number field sieve, and discuss the issue of the crossover point between these two methods.
The Magic Words Are Squeamish Ossifrage (Extended Abstract)
"... We describe the computation which resulted in the title of this paper. Furthermore, we give an analysis of the data collected during this computation. From these data, we derive the important observation that in the final stages, the progress of the double large prime variation of the quadratic siev ..."
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Cited by 2 (0 self)
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We describe the computation which resulted in the title of this paper. Furthermore, we give an analysis of the data collected during this computation. From these data, we derive the important observation that in the final stages, the progress of the double large prime variation of the quadratic sieve integer factoring algorithm can more effectively be approximated by a quartic function of the time spent, than by the more familiar quadratic function. We also present, as an update to [15], some of our experiences with the management of a large computation distributed over the Internet. Based on this experience, we give some realistic estimates of the current readily available computational power of the Internet. We conclude that commonlyused 512bit RSA moduli are vulnerable to any organization prepared to spend a few million dollars and to wait a few months.
Factoring Integers Above 100 Digits Using Hypercube MPQS
, 1995
"... In this paper we report on further progress with the factorisation of integers using the MPQS algorithm on hypercubes and a MIMD parallel computer with 1024 T805 processors. We were able to factorise a 101 digit number from the Cunningham list using only about 65 hours computing time. We give new de ..."
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In this paper we report on further progress with the factorisation of integers using the MPQS algorithm on hypercubes and a MIMD parallel computer with 1024 T805 processors. We were able to factorise a 101 digit number from the Cunningham list using only about 65 hours computing time. We give new details about the hypercube sieve initialisation procedure and describe the structure of the factor graph that saves a significant amount of computing time. At March 3rd, we finished the factorisation of a 104 digit composite.
Parallel Buchberger Algorithms on Virtual Shared Memory KSR1
, 1994
"... We develop parallel versions of Buchbergers Gröbner Basis algorithm for a virtual shared memory KSR1 computer. A coarse grain version does Spolynomial reduction concurrently and respects the same critical pair selection strategy as the sequential algorithm. A fine grain version parallelizes polynom ..."
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We develop parallel versions of Buchbergers Gröbner Basis algorithm for a virtual shared memory KSR1 computer. A coarse grain version does Spolynomial reduction concurrently and respects the same critical pair selection strategy as the sequential algorithm. A fine grain version parallelizes polynomial reduction in a pipeline and can be combined with the parallel Spolynomial reduction. The algorithms are designed for a virtual shared memory architecture and a dynamic memory management with concurrent garbage collection implemented in the MAS computer algebra system. We discuss the achieved speedup figures for up to 24 processors on some standard examples.
MIMDFactorisation on Hypercubes
, 1994
"... This paper describes the development and implementation of the MPQS factoring algorithm using multiple hypercubes customised to a MIMD parallel computer. The computationally most expensive steps ran on a Parsytec machine consisting of 1024 Inmos T805 microprocessors. General 100 decimal digit number ..."
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This paper describes the development and implementation of the MPQS factoring algorithm using multiple hypercubes customised to a MIMD parallel computer. The computationally most expensive steps ran on a Parsytec machine consisting of 1024 Inmos T805 microprocessors. General 100 decimal digit numbers can be factored in 12 days.