* Georgi Guninski:

> would prefer to keep my secrets encrypted with algorithm whose breaking
> requires *provable* average runtime x^4242 or even x^42 instead of 
> *suspected runtime* 2^(x/4).

It depends on the constant factors you omitted, including those in the
lower-order terms. 8-)

AES can be broken with O(1) effort, but the constant is so huge that
it's considered impractical.  IIRC, OpenPGP has an upper bound for key
length, too, so it too can be broken with O(1) effort as well.
Obviously, this isn't particularly meaningful.

For actually breaking algorithms, all that matters is the actual
running time of an attack, and the necessary storage capacitiy.
Big-O notation and complexity classes are not very helpful.

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