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Let's say I'm given a number.
I am now asked to determine if this number is of the form : $a^{b}$ mod $N$ .
Unfortunately the parameters are such that I cannot perform a discrete logarithm in feasible time. $a$ and $N$ are known (and large) natural numbers with $a<b<N$.
$a$ is a prime number. $N$ is composite. Nothing is known about $b$.
What are some mathematical tests I can perform to determine this?

Poneratoxin Mandera
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  • This is basically the Discrete Logarithm Problem. https://en.wikipedia.org/wiki/Discrete_logarithm – Joshua Wang Nov 15 '20 at 19:47
  • Welcome to Maths SX! Is $N$ prime? If not, you may try to simplify the problem using the Chinese remainder theorem. – Bernard Nov 15 '20 at 19:48
  • Thank you @Bernard! I've edited the question to include those details. N is composite. Thanks @JoshuaWang. I am aware of the discrete logarithm problem but N is chosen such that computing the discrete logarithm isn't feasible. – Poneratoxin Mandera Nov 15 '20 at 19:52
  • The number $c$ can be expressed in that way if GCD(N,c) = 1. – Count Iblis Nov 16 '20 at 06:48

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