Comment by ArcHound
1 day ago
But you can still analyse the behaviour of the values to identify backdoor behaviour rather than insisting on uncovering the exact method od generation.
Just seems to me like that's quite low on the priority list. I guess this result assures some people that the values are good.
An ideal backdoor would have completely invisible behavior to anyone that doesn't know the key.
you (mostly) can't. In computing, "random" is a property of a process to generate a number, not a property of a number itself. You cannot directly analyze a number to determine it has been randomly generated.
There are some caveats here. There are some intrinsic properties of numbers that random numbers satisfy with high probability, e.g. having high kolmogorov complexity. But these are generally very difficult to compute, and I would personally guess you could concoct (probably artificial) scenarios where
1. picking parameters randomly yields a secure construction, but
2. there exists a parameter set with high kolmogorov complexity that is insecure.
e.g. "high kolmogorov complexity", while being a property of random numbers, is generally not viewed as nearly as useful as being randomly generated (which is exhibited by saying generator + seed = the particular number, like in this article).
Sure, I agree. I'm mostly looking for backdoors as the goal, not identifying generation algorithm.
And yes, knowing what numbers are bad so that we avoid them is a good goal.