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Topic: Help with a factorisation, Please [Important]
Replies: 27   Last Post: Jan 26, 2014 9:33 AM

 Messages: [ Previous | Next ]
 David Bernier Posts: 3,892 Registered: 12/13/04
Re: Help with a factorisation, Please [Important]
Posted: Jan 24, 2014 10:50 AM

On 01/18/2014 04:13 PM, Port563 wrote:
> "David Bernier" <david250@videotron.ca> wrote in message
> news:lbem7l\$2nk\$1@dont-email.me...

>> On 01/18/2014 01:27 PM, Port563 wrote:
>>> Hlauk wrote:
>
>>> The fact remains that "your" composites, if entered into the Alpertron
>>> applet (after their consitutent prime pair has been multiplied out, so
>>> what I enter into the applet does _not_ have a "*" in it) are very easy
>>> to factorise, while the original composite chosen by David Bernier is
>>> not.
>>>
>>> Try it for yourself, please. In this order!
>>>
>>> Choose one of your pairs yourself.
>>>
>>> Multiply them out using something other than the Alpertron applet.
>>>
>>> Put the product into http://www.alpertron.com.ar/ECM.HTM and, having
>>> switched
>>> the number of threads to the maximum for your CPU(s), factorise it.
>>>
>>> Depending on the power of your PC, it will do it taking from under 1
>>> second
>>>
>>> Now take the 130 digit composite supplied by David. Use the applet to
>>> factorise
>>> it.
>>>
>>> Go and make some coffee.
>>>
>>> Have a walk.
>>>
>>> Do some gardening.
>>>
>>> Then even bake a cake? If your PC is old, you will have time.
>>>
>>> I think you will then see my point.
>>>
>>> If they appear to be of a different type from the POV of the applet, then
>>> they _are_ of a different type.
>>>
>>> It follows that either there is something unusual about your prime pairs,
>>> or

>>
>> I have a large collection of pseudo-random bytes, going back
>> to a video capture (on a few occasions) of "snow" or
>> "white noise" on a CRT tube. I mixed the bytes using recommended
>> procedures/heuristics. A 130 digits modulus was chosen,
>> ago with CADO-NFS 1.0 .
>>
>> Following Pubkeybreaker's ECM and quadratic sieve threat
>> discussion, I decided on two 65-digit primes.
>> I extracted digits from a base64 encoding of "random bytes"
>> by hand, and finally obtained two large enough 65-digit
>> pseudo-random numbers m1 and m2
>> (meaning that the product was 130 digits).
>>
>> Using PARI/gp, I tested for primality the next few thousand
>> odd numbers after the pseudo-random 'm1' and 'm2'.
>>
>> This gave the primes p > m1 , and q > m2, with
>> p*q having 130 digits.
>>
>> So, p and q are "nothing-up-my-sleeve" 65-digit primes.
>> I guess they were selected through partly noise-dependent
>> procedures, anyway I didn't interfere to cause bias.
>>
>> There are, from what I recall,
>> weak rsa moduli (unrelated to NSA work on promoting
>> "fake" rng generators). I didn't test for
>> "weak rsa moduli" in the original, pre-NSA-revelations,
>> sense.

>
>
>
> I was sure there was nothing peculiar about your 130 bit "nearly prime",
> David.
>
> The time it takes to be broken is what I would expect for a nearly prime of
> that size whose prime factors are of approximately the same magnitude.
>
> It is Dan's pairs that are peculiar!
>
>
>
>
>
>
>
>
>

My CADO-NFS 2.0 job with Perl script broke down with an error.
So, now I come clean with the truth:

69176818182079702962583905305944091851396378426614231238000704281*68643130470496608225965397098921704892910199186048409746525386899
47485133560063190433548259679204355907477810307482663990525310023918\
21388435849831808696657092215642611599144927466443608010614619

quit

dave

--

Date Subject Author
1/18/14 Daniel Joyce
1/18/14 Port563
1/18/14 Daniel Joyce
1/18/14 Daniel Joyce
1/18/14 Port563
1/18/14 David Bernier
1/18/14 Daniel Joyce
1/18/14 Port563
1/18/14 Daniel Joyce
1/18/14 Port563
1/18/14 Port563
1/18/14 Daniel Joyce
1/18/14 Daniel Joyce
1/19/14 Daniel Joyce
1/19/14 Port563
1/19/14 Daniel Joyce
1/24/14 David Bernier
1/24/14 Daniel Joyce
1/24/14 Port563
1/24/14 David Bernier
1/25/14 Port563
1/25/14 Port563
1/25/14 Daniel Joyce
1/25/14 Port563
1/25/14 Daniel Joyce
1/25/14 Port563
1/26/14 Daniel Joyce