Re: JSH: What are you people?

On 23 Jan, 18:57, Rotwang <sg...@xxxxxxxxxxxxx> wrote:
On 23 Jan, 17:23, Rotwang <sg...@xxxxxxxxxxxxx> wrote:



RSA numbers usually have at least 1024 bits. The smallest number of
distinct primes whose product is larger than 2^1024 is 132. 25% of 132
is 33. That means that, even if your 75% estimate were correct
(*which* *it* *isn't*) you would be attempting to reconstruct a factor
of T from its values mod p_n, with the expectation that 33 of those
values were wrong. So what do you do? Assume that 99 of them are
correct and try every combination of 99 chosen from 132? There are
more than 10^31 of those, and each one only partially narrows down the
candidates for trial factors < sqrt(T). That doesn't sound to me like
a trivial solution to the factoring problem.

Increment the oops counter. I should have been looking for the
smallest number of distinct primes whose product is greater than
2^512. Since I am now at home and don't have Mathematica at my
disposal I don't know what that is, and can't be bothered to work it
out. Though in practice it doesn't matter; Wikipedia says that it is
currently recommended that the keys used be at least 2048 bits long,
so my previous calculation applies.

You know that sound one makes when one places one's tongue behind
one's lower lip to indicate that something stupid has been said? I
really want to write that in response to the above but I'm not sure
how to spell it. My best guess is "mmmmmnnnggh". 132 is obviously not
the smallest number of distinct primes whose product is greater than
2^1024, but rather the smallest number n such that the product of the
first n primes is greater than 2^1024.

Sorry. In my defence it's my birthday and I'm wasted. Don't drink and
derive, etc.
.