1. I understand the concept of discrete logs, but I had a hard time following any of the methods to compute them. Under the "computing discrete logs mod 4" section, I don't understand the conclusion which says "if we believe that finding discrete logs for p congruent to 3 (mod 4) is hard, then so is computing such discrete logs (mod 4). Nor did I understand the lemma presented in this section. I was able to follow the Pohlig-Hellman Algorithm for about the first half. When it starts saying x=x_1+x_2q+..., I don't really get it.
2. I liked the Index Calculus. I basically understood this method. My question is, what makes one of these methods more useful than the others? Also, when will a public key where the trapdoor is finding discrete logs be more useful than RSA?
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