One of the one$-$way functions used in public key cryptography is the discrete logarithm. Computing r$$gemodp

from g$,$e$,$

and p

is easy. But given only r

$,$ g

and p

$,$ recovering e

is hard.

Suppose p$=1277$

$,$ g$=3$

and r$=705$

$.$

What is the smallest positive integer e

such that r$$ge mod p

$?$