key length/size RSA discussion/recommendations in the wiki

Robert J. Hansen rjh at
Wed Oct 29 22:30:56 CET 2014

> No, I'm using a strict definition of brute force.

Technically, brute force is testing every *possible* value... not values
that you know aren't going to work.  Why test those?

If you're trying to factorize 2701, for instance, you can feel free to
skip dividing by 2 (doesn't end in an even number), 3 (sum of the digits
isn't divisible modulo three), 4 (already know it's not divisible by 2),
5 (doesn't end in a 5 or a 0), 6 (not divisible by 3 or by 2), etc.

If your brute-forcer is testing values that cannot possibly be correct,
then you're using an inefficient brute-forcer.  Get a better one.  :)

> I don't feel the method outlined by Rob is still brute force. That
> brute actually is using his brain. Possibly his brain resembles a
> sieve, but still :). Am I too strict?

Depends.  I think so.  But if you're taking an exam sometime in the near
future, I think you should answer this however your professor wants.  :)

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