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>The number of randomly selected 768 bit primes that you would need for a >reasonable chance of a birthday collision is 1.708E104 True however the current mechanism of generating PGP keys which consists primarily of pseudo-randomly pounding on a keyboard is hardly "truely random. Have no idea of the true number but expect it to be significantly less than that quoted above, even for a 1024 bit key like mine. Warmly, Padgett
A. Padgett Peterson P.E. Information Security wrote: | >The number of randomly selected 768 bit primes that you would need for a | >reasonable chance of a birthday collision is 1.708E104 | | True however the current mechanism of generating PGP keys which consists | primarily of pseudo-randomly pounding on a keyboard is hardly "truely random. | | Have no idea of the true number but expect it to be significantly less than | that quoted above, even for a 1024 bit key like mine. Accroding to Stephan Neuhaus's 'Statistical Properties of IDEA session keys in PGP,' the session keys are very well distributed, when tested for equidistribution and serial correlation. This does not demonstrate that the RSA keys are as well distributed, but it does generate some confidence that the key generation methods of PGP are not very broken. Testing for RSA generation would be more difficult, since there are some practical difficulties in getting a large sample of RSA private keys. Stephan Neuhaus is neuhaus@informatik.uni-kl.de. He has a long (24 page), and short (8? page) version of the paper available. Adam -- "It is seldom that liberty of any kind is lost all at once." -Hume
Here is a good idea for random numbers: Take a piece of non conducting board, say about six by six feet. Put electrodes on it; say a pair of electrodes every quarter inch or so across and down. Each pair of electrodes would be connected to logic so that it generates a unique number. When the electrodes are shorted, the number would be generated. Put this contraption out in the rain. As raindrops fall on the board with electrodes, the water would conduct and short the electrodes. Rain falls in a totally random manner. As raindrops hit the electrodes, they would momentarily short and cause a number to be generated. Yout would get a random series of numbers. Now, as it does not rain in the same place all the time, a network of these rain random generators could be set up troughout the land and be hooked up on the Internet. Each one would be sort of a rain random number server. These servers would cooperate. They would notify each other when one has rain raining on it and another one would not. We could have a series of master servers, or dispatcher. The dispatchers would work cooperatively and collectively know which rain random generator has rain raining on it and is generating random numbers. It would be up to the client, who is needing random numbers to access the rain random generators that are operating. All of this could be done in real time using current client server technology. In fact, since it is allways raining in more than one part of the world at any given time, many rain random generator servers would be available at any time. The master servers, or dispatchers, would have a constant running list of active generators. What do you all think? Mark Allyn allyn@allyn.com http://mark.allyn.com http://clearplastic.com