5 ms·

While perhaps not an advance, the algorithms implemented are state-of-the-art (GNFS, Pollard's p-1 test, Williams' p+1 test, cyclotomic polynomial test). But w

While perhaps not an advance, the algorithms implemented are state-of-the-art (GNFS, Pollard's p-1 test, Williams' p+1 test, cyclotomic polynomial test). But whatever the running times, it is an astounding artifact.

daoudc 15y ago
There is a year or two of work on top of the documentation I have included. Also, I think it is likely that there are some incremental improvements to the existing algorithms that my uncle put in place without necessarily documenting. Whilst these might not be theoretically interesting, their combined effect could be significant. There may also be some new maths in there too, as he was undoubtedly a brilliant mathematician.
- ronnier 15y ago
  Do you have any kind of bio on him? Even a picture?
  - daoudc 15y ago
    I'm hoping to get both of these. It needs some collaboration with my family to do it properly.
wbhart 15y ago
It's remarkable that we refer to algorithms invented as "late" as the 90's as state-of-the-art. But sadly, it is so.
- primecommenter 15y ago
  Even more remarkable is that they build directly upon the 400-year-old method of Fermat (http://en.wikipedia.org/wiki/Fermat%27s_factorization_method http://en.wikipedia.org/wiki/Fermat%27s_factorization_method).
  - pbsd 15y ago
    Well, directly is a bit of a stretch. It's probably more fair to say they're directly based off the Powers-Lehmer-Morrison-Brilhart (also Kraitchik, for the discrete log) method, which introduced the concept of factor bases and combining relations to find a difference of squares.
- archgoon 15y ago
  The officially published ones. It remains an open question what the NSA knows. I was going to back up the idea that the NSA might potentially be ahead of the public community of number theorists and cryptographers by citing the relative sizes of the two groups. Unfortunately, those numbers are classified. :(
  - wbhart 15y ago
    The NSA recently stated that they are only a couple of years ahead. And by that I take it they mean their computers are bigger. Recall that they are a military outfit. Only a small part of what they do is crypto related. Despite them having 40,000 employees or so, one shouldn't read that as meaning they have 40,000 people working on breaking RSA. They do many other things.

daoudc 15y ago

There is a year or two of work on top of the documentation I have included. Also, I think it is likely that there are some incremental improvements to the existing algorithms that my uncle put in place without necessarily documenting. Whilst these might not be theoretically interesting, their combined effect could be significant. There may also be some new maths in there too, as he was undoubtedly a brilliant mathematician.

ronnier 15y ago
Do you have any kind of bio on him? Even a picture?
- daoudc 15y ago
  I'm hoping to get both of these. It needs some collaboration with my family to do it properly.

wbhart 15y ago

It's remarkable that we refer to algorithms invented as "late" as the 90's as state-of-the-art. But sadly, it is so.

primecommenter 15y ago
Even more remarkable is that they build directly upon the 400-year-old method of Fermat (http://en.wikipedia.org/wiki/Fermat%27s_factorization_method http://en.wikipedia.org/wiki/Fermat%27s_factorization_method).
- pbsd 15y ago
  Well, directly is a bit of a stretch. It's probably more fair to say they're directly based off the Powers-Lehmer-Morrison-Brilhart (also Kraitchik, for the discrete log) method, which introduced the concept of factor bases and combining relations to find a difference of squares.
archgoon 15y ago
The officially published ones. It remains an open question what the NSA knows. I was going to back up the idea that the NSA might potentially be ahead of the public community of number theorists and cryptographers by citing the relative sizes of the two groups. Unfortunately, those numbers are classified. :(
- wbhart 15y ago
  The NSA recently stated that they are only a couple of years ahead. And by that I take it they mean their computers are bigger. Recall that they are a military outfit. Only a small part of what they do is crypto related. Despite them having 40,000 employees or so, one shouldn't read that as meaning they have 40,000 people working on breaking RSA. They do many other things.