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<p style="margin-bottom:.0001pt">Hallo cryptografers,</p>
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<p style="margin-bottom:.0001pt">I’m searching for someone who may help me by writing a little program for factoring large composite numbers.</p>
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<p style="margin-bottom:.0001pt">I’ve been into primes for a couple of years now and have discovered a structure that enables one to factorize composite numbers in a special way. It starts directly under the squareroot of a given integer and works backwords from that point through the possible factors. And it’s working <u>very</u> fast at the beginning (while checking the highest possible factors) and is then slowing down constantly until it reaches the very small factors (like 101), where it is still working properly but it’s definitely to slow and not longer useful in a practical way.</p>
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<p style="margin-bottom:.0001pt"> RSA 250 was the chosen number to describe the method using that integer as an example. It is known that the prime factors of RSA 250 are primes of the form 6n – 1, that is why the description of the method is basicly focused on this group of possible factors (but it also works for factors of the type 6n + 1 , slightly modified of course).</p>
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<p style="margin-bottom:.0001pt">The “General Number Field Sieve” and its variations are the fastest methods for the factorization so far. Used as an alternative start the method I found should be <u>faster</u> as the General Number Field Sieve – up to a certain point, of course (while checking the biggest factors).</p>
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<p style="margin-bottom:.0001pt">Let us look at RSA 250 as an example to get an idea of the speed of this alternative approach:</p>
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<p style="margin-bottom:.0001pt">RSA 250 is a number with 250 decimal digits. Using the method I’m talking about it’s possible to check the first group of</p>
<p style="margin-bottom:.0001pt">20831160293131638348898886842852463138276835849237265490215514 factors (of the form 6n – 1)</p>
<p style="margin-bottom:.0001pt">with the result that non of them divides RSA 250. That procedure will take only a few minutes when calculated <u>manually</u> (like I have to do), checking that group of 2.08 * 10^61 factors in the first round. The next group of possible factors is a little bit smaller, so the whole thing starts slowing down step by step (as said at the beginning).</p>
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<p style="margin-bottom:.0001pt">If one takes a much bigger number with 2500 decimal digits for example, the number of checked integers in the first group is <u>increasing</u> – so the method becomes <u>faster</u> than before (again: we’re looking only at the biggest possible factors at the moment). A randomly chosen integer of that size (not divisible by 2 and 3) will cost between 10 and 100 times more calculating power for the first round (compared with RSA 250) but the method will check approximately 10^623 (!) possible factors at one time (that’s the average amount at the beginning).</p>
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<p style="margin-bottom:.0001pt">If you think that this is fast than it’s worth programming (and if not: please let me know). Sadly I’m not capable to do so. The used structure and the used algorithm is easy to understand, so it should be easy to implement the whole thing, too. I’m searching for someone who is willing to do so and who can estimate (or calculate) the number of used <u>elementary operations</u> as well, to compare this sieve with the other known methods.</p>
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<p style="margin-bottom:.0001pt">Thank you for reading so far. If someone can help, please contact me. (Shall I post my e-mail-address or is there another way to get in contact?)</p>
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<p style="margin-bottom:.0001pt">Please excuse any funny mistakes for English isn’t my natural language.</p>
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<p style="margin-bottom:.0001pt">Kind regards</p>
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<p style="margin-bottom:.0001pt">Helge Wißmann (born in Germany, living in Switzerland)</p>
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<p style="margin-bottom:.0001pt">PS: The mathematical background and the resulting structure for a program has been published as a little book a few days ago in Germany: Ein Beitrag zur Faktorisierung von RSA 250 ISBN 978-3-7528-8619-1; </p>
<p style="margin-bottom:.0001pt">Those who are interested in the matter may recieve a digital preprind for free.</p>
<p style="margin-bottom:.0001pt">And I'll try to translate it into english, if nessecary.</p>
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