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In this paper we give a consistent and simple proof for the XOR-Lemma which was hinted at by Yao in 3] and subsequently presented by him in lectures. It can be found in print in 2]. By the lemma we know that the security of any one-way function f : X ?! f0; 1g can be substantially ampliied if the function is replaced by the XOR with itself, namely by f f :(More)
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 1{2 days.
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(More)
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