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Cryptography

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    $\begingroup$ I considered a similar approach to your partial factorization method, however I was under the impression that while random large integers $S^e - Pad_n(M)$ often had small factors, they rarely had enough to make up a total of 1024 or 2048 bits. Do you have a guess of the success probability? $\endgroup$ Commented Jun 29, 2013 at 13:57
  • $\begingroup$ @poncho: I have no quantitative derivation of up to what $n$ the idea might realistically work. With free supply of $M$ and a number of $S$ having their high bit clear, I'm optimistic for $n=768$, perhaps much more. See extensive changes. $\endgroup$ Commented Jun 29, 2013 at 16:03
  • $\begingroup$ Note: If you didn't intend to make this "community wiki" you can flag this for a moderator to undo that... and you can continue to gain reputation for the posting. $\endgroup$ Commented Jul 4, 2013 at 19:47
  • $\begingroup$ @makerofthings7: I don't care too much for reputation, for reputation can't buy me time. Yet I'm a serial editor, and occasionally ask a moderator to undo the consequences. $\endgroup$ Commented Jul 5, 2013 at 11:32