Re: Surrogate factoring, potential
- From: jt64@xxxxxxxx
- Date: 13 Mar 2007 13:18:17 -0700
On 13 Mar, 14:09, rossum <rossu...@xxxxxxxxxxxx> wrote:
On 12 Mar 2007 19:40:59 -0700, jst...@xxxxxxxxx wrote:
Example:
T = 732367903, k=24412263
Surrogate: 1191915704826532 = ( 4 )( 7 )( 73 )( 583129014103 )
f_1 = 7/2 and f_2 = 85136836059038
and 4f_1*f_2 = 2k^2 - 2T
y=-170273672118069/2 and x=170273623293557/2
so, x+y=-24412256, which has 223 as a factor.
T = 732367903 = (223)(3284161)
Iterations: 1
By my calculations 24412256 has 24 positive factor pairs:
(1, 24412256), (2, 12206128), (4, 6103064), (8, 3051532),
(11, 2219296), (16, 1525766), (22, 1109648), (32, 762883),
(44, 554824), (88, 277412), (176, 138706), (223, 109472),
(311, 78496), (352, 69353), (446, 54736), (622, 39248),
(892, 27368), (1244, 19624), (1784, 13684), (2453, 9952),
(2488, 9812), (3421, 7136), (3568, 6842), (4906, 4976)
That is 48 positive factors and another 48 negative ones, 96 possible
factors. How did you come to select 223 as the first one to try? Why
did you not pick 4906 or -311 to start with? On average you would
expect to have a number of wrong selections before hitting on the
right one.
Notice that with the surrogate factored there was not even a lot of
iterating through combinations of those factors, as it took one try.
Why? You have given no reason for starting with 223. What criteria
are you using to select the order in which you try factors?
That example is the potential, as it could be a much larger target,
where the primary issue is factoring the surrogate.
With the surrogate factored, looping through all the iterations of
factors the theory says you have a 50% chance of factoring, so, if I
got the mathematical theory right, anybody with some serious factoring
power already could convert maybe even an RSA sized number into
several surrogates, go at it, and just walk away with a factorization,
just like that.
You can program in Java, and Java has a BigNum package. You could
easily program it yourself. If you are worried about factoring a new
RSA number, then factor one that has already been factored such as
RSA-576 or RSA-640. You will show that your method works and will not
have any effect on the stock market.
rossum- Dölj citerad text -
- Visa citerad text -
Stupid people do not understand compiled code left on the computer by
JSH, stupid people do not know how to reverse engineer compiled
algorithms. Stuipid people will never factor any RSA number.
Oh that is just my bet, i think people been factoring RSA for years
but been wise enough not to talk about it.
My guess is that the people with the bignum source code factored alot
of things, but stupid people try to find out the source code they
factor nothing because the compiled code have not bignum library, and
stupid people do not understand how to write algorithms and equation
from binaries.
So given an effective algorithm how many important messages have been
read now since -97 quite a few i would guess.
On the other hand my thought on the subject is that it is actually
easy to factor prime products. Given the correct algorithm, so maybe
the algorithm just was for stupid pesants anyway, and no really top
secret messages use it.
For someone who wants to read stupid pesants message traffic a rumour
of hardness of the factoring of prime products of course would be a
bless of god.
And maybe they think they are.
JT
.
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- Re: Surrogate factoring, potential
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- Re: Surrogate factoring, potential
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