power of a matrix

[GUSTAVO TERRA BASTOS]

Hi !

Given square matrices M, N over large finite fields, is there an easy way to compute the positive integer so that M^i = N ?

Best regards,

Gustavo   

[Dima Pasechnik]

On Thu, Mar 17, 2022 at 12:23 PM GUSTAVO TERRA BASTOS
<gtba...@ufsj.edu.br> wrote:
>
> Hi !
>
> Given square matrices M, N over large finite fields, is there an easy way to compute the positive integer so that M^i = N ?
>

this is known as a discrete logarithm problem, and no fast algorithms are known.
https://en.wikipedia.org/wiki/Discrete_logarithm

There is however a necessary condition, that M and N commute, i.e.
MN=NM, which is certainly fast
to check.



> Best regards,
> Gustavo
>
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