How to print all expressions that match a regular expression

[hzhuo1 at gmail.com]

>
> And I really don't see how simple enumeration of range(2^2048) breaks
> RSA-2048, since that problem requires you to find two factors which,
> when multiplied together, give that specific value.
>

I can tell you why is that. RSA-2048 has a composite of length less
than 2^2048, which is a product of two large primes. So one of its
factors cannot exceed 2^2047, and we can treat the multiplication as a
computation with constant complexity. So the time complexity of
enumerating 2^2048 strings is the same with factoring a composite with
length 2^2048 which is the product of two primes.

And obviously, whenever we successfully factor the composite, we can
calculate the Euler function of it. So that given any public key
(n,e), calculating the private key (n,d) is easy.