## Predicted partial factorization of RSA-576

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• Someone who may wish to remain nameless, so I m not revealing his/her name or email address, sent me this prediction recently. ... It will be interesting to
Message 1 of 8 , Jun 29, 2004
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Someone who may wish to remain nameless, so I'm not revealing his/her
name or email address, sent me this prediction recently.

> I have computed that the first 10 digits of RSA 768 as
>
> 57688 02668 and
>
> 21324 81819

It will be interesting to see whether this prediction is
borne out. We should find out within a year or two. In the
mean time, the prediction will be saved here for posterity.

Paul
• ... Presumably there s a typo and this person means 5768802686 instead of 5768802668 as 5768802668999999999... * 2132481819999999... = 123018668148... which is
Message 2 of 8 , Jun 29, 2004
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--- In primenumbers@yahoogroups.com, "Paul Leyland" <pleyland@m...>
wrote:
> Someone who may wish to remain nameless, so I'm not revealing
> his/her name or email address, sent me this prediction recently.
>
> > I have computed that the first 10 digits of RSA 768 as
> >
> > 57688 02668 and
> >
> > 21324 81819
>
>
> It will be interesting to see whether this prediction is
> borne out. We should find out within a year or two. In the
> mean time, the prediction will be saved here for posterity.

Presumably there's a typo and this person means
5768802686
5768802668
as

5768802668999999999... * 2132481819999999... =
123018668148...
which is clearly smaller than the required RSA 576 challenge number of
123018668453...

Hope that helps!

Richard Heylen
• Another observation: I presume that both factors have the same numbers of bits, that means that of both numbers the most significant bits and the least
Message 3 of 8 , Jun 29, 2004
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Another observation:

I presume that both factors have the same numbers of bits,
that means that of both numbers the most significant bits and the least significant bits are all 1's.

If this is so, than the quotient N1/N2 must be greater than 0,5 and less then 2.

As 57/21 > 2, I would not bet on these numbers !!!

Henk van der Griendt
----- Original Message -----
From: richard_heylen
Sent: Tuesday, June 29, 2004 4:01 PM
Subject: [PrimeNumbers] Re: Predicted partial factorization of RSA-576

--- In primenumbers@yahoogroups.com, "Paul Leyland" <pleyland@m...>
wrote:
> Someone who may wish to remain nameless, so I'm not revealing
> his/her name or email address, sent me this prediction recently.
>
> > I have computed that the first 10 digits of RSA 768 as
> >
> > 57688 02668 and
> >
> > 21324 81819
>
>
> It will be interesting to see whether this prediction is
> borne out. We should find out within a year or two. In the
> mean time, the prediction will be saved here for posterity.

Presumably there's a typo and this person means
5768802686
5768802668
as

5768802668999999999... * 2132481819999999... =
123018668148...
which is clearly smaller than the required RSA 576 challenge number of
123018668453...

Hope that helps!

Richard Heylen

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• ... 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,
Message 4 of 8 , Jun 29, 2004
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> Presumably there's a typo and this person means
> 5768802686
> 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
• 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
Message 5 of 8 , Jun 29, 2004
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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
> > 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
>
>
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
>
>
>
>
>
• Yes, RSA-768. My typo. I ve 576 on the mind these days. My conclusion still holds, once that silly typo is fixed. Paul
Message 6 of 8 , Jun 29, 2004
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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
> > > 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
> >
> >
> > ------------------------ Yahoo! Groups Sponsor
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> --------------------------------------------------------------
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> >
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• The factor of 2 seems not to be true if one prime can be one bit shorter, consider 1111111....1 divided by 100000...1 which is closer to 3. Milton L. Brown
Message 7 of 8 , Jun 29, 2004
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The factor of 2 seems not to be true if one prime can be one bit shorter,
consider

1111111....1 divided by
100000...1

which is closer to 3.

Milton L. Brown
miltbrown@...

For the factors of RSA 140:

6.2642e69 = 2^231.8601
3.3987e69 = 2^230.9780

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

Yes. Explicitly

3398717423028438554530123627613875835633986495969597423490929302771479 =
1111110000100001100000001100100110111010010011101100010010110111101000\
1000101010100011111101111010000111110010100000000100010010010001010001\
0100100111100010001011011011010011010010100110110011100010011001101100\
001010001011100010111
6264200187401285096151654948264442219302037178623509019111660653946049 =
1110100001011010001000110010001011111010010101101000000001110101011110\
0101100111001110000100000101100000001001001001001011001111011110111010\
1110001011000010010010110010011100000010000110000101001111011101001110\
0011001010010011000001

> [Original Message]
> From: Henk van der Griendt <henk@...>
> Date: 6/29/2004 11:15:21 AM
> Subject: Re: [PrimeNumbers] Re: Predicted partial factorization of RSA-576
>
> Another observation:
>
> I presume that both factors have the same numbers of bits,
> that means that of both numbers the most significant bits and the least
significant bits are all 1's.
>
> If this is so, than the quotient N1/N2 must be greater than 0,5 and less
then 2.
>
> As 57/21 > 2, I would not bet on these numbers !!!
>
> Henk van der Griendt
> ----- Original Message -----
> From: richard_heylen
> Sent: Tuesday, June 29, 2004 4:01 PM
> Subject: [PrimeNumbers] Re: Predicted partial factorization of RSA-576
>
>
> --- In primenumbers@yahoogroups.com, "Paul Leyland" <pleyland@m...>
> wrote:
> > Someone who may wish to remain nameless, so I'm not revealing
> > his/her name or email address, sent me this prediction recently.
> >
> > > I have computed that the first 10 digits of RSA 768 as
> > >
> > > 57688 02668 and
> > >
> > > 21324 81819
> >
> >
> > It will be interesting to see whether this prediction is
> > borne out. We should find out within a year or two. In the
> > mean time, the prediction will be saved here for posterity.
>
> Presumably there's a typo and this person means
> 5768802686
> 5768802668
> as
>
> 5768802668999999999... * 2132481819999999... =
> 123018668148...
> which is clearly smaller than the required RSA 576 challenge number of
> 123018668453...
>
> Hope that helps!
>
> Richard Heylen
>
>
>
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
>
>
>
>
>
>
>
>
>
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• Milton Yes but you have not addressed Richard Heylen s observation that say (5768802668 + 1) * (2132481819 + 1) = 12301866814809977580 whose 12 leading digits
Message 8 of 8 , Jun 30, 2004
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Milton

Yes but you have not addressed Richard Heylen's observation that say

(5768802668 + 1) * (2132481819 + 1) = 12301866814809977580

whose 12 leading digits are less than the 12 leading digits of RSA 576
which are 123018668453... ?

Regards

Alan Powell

> > From: richard_heylen
> > Sent: Tuesday, June 29, 2004 4:01 PM
> > Subject: [PrimeNumbers] Re: Predicted partial factorization of RSA-576
> >
> >
> > --- In primenumbers@yahoogroups.com, "Paul Leyland" <pleyland@m...>
> > wrote:
> > > Someone who may wish to remain nameless, so I'm not revealing
> > > his/her name or email address, sent me this prediction recently.
> > >
> > > > I have computed that the first 10 digits of RSA 768 as
> > > >
> > > > 57688 02668 and
> > > >
> > > > 21324 81819
> > >
> > >
> > > It will be interesting to see whether this prediction is
> > > borne out. We should find out within a year or two. In the
> > > mean time, the prediction will be saved here for posterity.
> >
> > Presumably there's a typo and this person means
> > 5768802686
> > 5768802668
> > as
> >
> > 5768802668999999999... * 2132481819999999... =
> > 123018668148...
> > which is clearly smaller than the required RSA 576 challenge number of
> > 123018668453...
> >
> > Hope that helps!
> >
> > Richard Heylen

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