Solve for x in $a = x^b$ (mod n)

Question

I would like to solve for $x$ in $a = x^b\ (mod\ n)$ given $a$, $b$, $n$. How might I go about doing this?

That answer primarily covers square roots, it doesn't seem to well cover a generalized case where b is some arbitrary integer. — Bradley Evans, Apr 22 '17 at 06:01

score 0 · Accepted Answer · answered Apr 22 '17 at 04:37

0

In general there is no such method.

Are the numbers small enough to brute force? Can you factor $n$?

answered Apr 22 '17 at 04:37

yberman

In the specific case I'm working (bit of a tricky personal cryptanalysis brain teaser) n is known to be the product of primes p and q (n is semi-prime), and n is sufficiently large to make brute force unfeasible. b is quite small, however (in my particular case, 5, but I was trying to come up with a more general picture). – Bradley Evans Apr 22 '17 at 06:06
Do you know $p$ and $q$? – yberman Apr 22 '17 at 13:47
No, unfortunately. – Bradley Evans Apr 23 '17 at 17:23
So you are basically trying to undo RSA? – yberman Apr 23 '17 at 21:33

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