In Q2: What is "high probability"? Usually it means something along the lines of $\ge1-\frac{1}{2^n}$, but to do that I would need $O(poly(n)t(n))$ steps (the question states to use $O(t(n))$ steps). Do I have the algorithm wrong, or is some constant probability larger than $\frac{1}{2}$ also OK for this question?

In Q4:

- How do we get a prime p such that p-1 has a large prime factor? I dont see a way (other than getting a random p, and using sage to factor p-1 to check). Am I missing something (or perhaps it's something we havn't learned yet)? (perhaps something similar to Sophie Germain primes?)

- Just making sure: Do you mean to print $10^{82}$ and $10^{77}$ or is $10^{82}$ and $10^{72}$ correct? (I dont see why it would be interesting to compare q with $10^{72}$)

- The whole "visual comparison" comment seems somewhat irrelevant since we are using sage/python and not maple…

In Q5: Do you mean to solve DL for any instance with probability $\ge \frac{1}{2}$ ? because I dont see how to get exactly $\frac{1}{2}$.