let $z = a + bi$ where $a,b$ are integers on $[0,N)$ let $a + bi \mod t = (a \mod t) + (b \mod t) \cdot i$
Consider the problem of finding $e$ where $z^e \mod N = c$ and $c, N$ and $z$ are known. Is this problem of similar difficulty to the discrete logarithm problem? Could Shor's algorithm be used to solve it. Also, how would the difficulty of this problem change if z were to be a Quaternion or Octonion.