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Another Small Bit Question, RSA Numbers

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  • Milton Brown
    Sorry, another small question. For the factors of RSA 140: 6.2642e69 = e^231.8601 3.3987e69 = e^230.9780 Does this mean that the second number is one bit
    Message 1 of 1 , Jun 29, 2004
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      Sorry, another small question.

      For the factors of RSA 140:

      6.2642e69 = e^231.8601
      3.3987e69 = e^230.9780

      Does this mean that the second number is one bit shorter than the other?

      Also, for

      5.7688e115 = e^384.55
      2.1324e115 = e^383.11

      Thanks,

      Milton L. Brown
      miltbrown@...


      > [Original Message]
      > From: Paul Leyland <pleyland@...>
      > To: <miltbrown@...>; richard_heylen
      <rick.heylen@...>; <primenumbers@yahoogroups.com>
      > Date: 6/29/2004 7:52:06 AM
      > Subject: RE: [PrimeNumbers] Re: Predicted partial factorization of RSA-576
      >
      > Yes, RSA-768. My typo. I've 576 on the mind these days.
      >
      > My conclusion still holds, once that silly typo is fixed.
      >
      >
      > Paul
      >
      > > -----Original Message-----
      > > From: Milton Brown [mailto:miltbrown@...]
      > > Sent: 29 June 2004 15:40
      > > To: Paul Leyland; richard_heylen; primenumbers@yahoogroups.com
      > > Cc: miltbrown
      > > Subject: RE: [PrimeNumbers] Re: Predicted partial
      > > factorization of RSA-576
      > >
      > >
      > > Small question. RSA 768 right?
      > >
      > > Also, can't the numbers be one bit longer or smaller
      > > so 2^(384+/-1) ?
      > >
      > > Thanks,
      > >
      > > Milton L. Brown
      > > miltbrown at earthlink.net
      > > miltbrown@...
      > >
      > > > [Original Message]
      > > > From: Paul Leyland <pleyland@...>
      > > > To: richard_heylen <rick.heylen@...>;
      > > <primenumbers@yahoogroups.com>
      > > > Date: 6/29/2004 7:16:44 AM
      > > > Subject: RE: [PrimeNumbers] Re: Predicted partial
      > > factorization of RSA-576
      > > >
      > > >
      > > > > Presumably there's a typo and this person means
      > > > > 5768802686
      > > > > instead of
      > > > > 5768802668
      > > > > as
      > > > >
      > > > > 5768802668999999999... * 2132481819999999... =
      > > > > 123018668148...
      > > > > which is clearly smaller than the required RSA 576
      > > challenge number of
      > > > > 123018668453...
      > > >
      > > > It's possible that there was a typo, I don't know.
      > > >
      > > > I'm pretty sure that the digits given are much more wrong than that,
      > > though.
      > > >
      > > > RSA-576 is, by definition, a 576-bit number and suitable
      > > for a RSA public
      > > > modulus. 576-bit numbers lie in the range 2^575 to 2^576-1.
      > > >
      > > > The contest organizers tell us that the factors are both
      > > the same size in
      > > > bits, meaning that they are both 384-bit numbers and so
      > > both lie in the
      > > > range 2^383 to 2^384-1. All of the solved challenge
      > > factorizations have
      > > > two factors of equal size, and I see no reason to doubt
      > > that RSA-576 also
      > > > does.
      > > >
      > > > However, 2^383 is 19701....53408 and 2^384-1 is
      > > 39402....06817 from which
      > > > I conclude the larger factor is significantly smaller than the one
      > > > predicted by our mysterious (partial-)factoring expert.
      > > >
      > > >
      > > > Paul
      > > >
      > > >
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