## Another Small Bit Question, RSA Numbers

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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
Message 1 of 1 , Jun 29, 2004
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
> 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@...
> >
> > > [Original Message]
> > > From: Paul Leyland <pleyland@...>
> > > To: richard_heylen <rick.heylen@...>;
> > > 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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