Say we are given the following cyclic group $$G$$ which is generated by $$g$$ element of $$\mathbb{Z}_p$$. In this case $$g=13$$ and $$p=23$$ so $$13$$ element of $$\mathbb{Z}_{23}$$.

If there exists two random $$g$$ values in the cyclic group $$G$$, how does one go about computing the discrete log in $$G$$?

• – Zhaohui Du Aug 26 '19 at 3:27

Say $$g=8$$. Then since $$8\cong {13^2}\pmod{23}$$, we say the discrete log of $$8$$ with respect to the base $$13$$ mod $$23$$ is $$2$$.
You can write $$2=\operatorname {ind}_{13}8\pmod{23}$$. (Gauß called it the index.)