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This challenge is intended to track the state of the art in integer factorisation. A primary application is for choosing the Key Length of the RSA Public-key Encryption scheme. Progress in this challenge should give an insight into which Key Size s are still safe and for how long. As RSA Laboratories is a provider of RSA-based products, the challenge is used by them as an incentive for the academic community to attack the core of their solutions — in order to prove its strength. The first RSA numbers generated, from RSA-100 to RSA-500, were labeled according to their number of Decimal digits; later, however, beginning with RSA-576, Binary digits are counted instead. An exception to this is RSA-617, which was created prior to the change in the numbering scheme. THE MATHEMATICS Let ''n'' be an RSA Number. There are Prime Number s ''p'' and ''q'' such that : The problem is to find these two primes, given only ''n''. Let ''s'' be ; then the values of some basic Arithmetic Function s are : : : THE PRIZES AND RECORDS The following table gives an overview over all RSA numbers. The challenge numbers in pink lines are numbers expressed in Base 10 , while the challenge numbers in yellow lines are numbers expressed in Base 2 , and for which a cash prize is still assigned. |
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