6.5-6.7 and 7.1, Due on October 27

The most interesting portion of these sections for me was the idea of trapdoors. I liked reading about the variety of trapdoors available and how they differ according to the public key system. I also enjoyed reading about other types of public key cryptosystems besides the RSA. It's easy to avoid thinking outside the box but this section helped me see some other alternatives to the RSA.
One thing I didn't really understand was the discrete logs in section 7.1. I am familiar with the idea of logarithms but I don't understand the x=L[subalpha](Beta) notation. I also don't really see how the discrete logs apply to anything so far. I imagine their application will become more apparent in the ensuing sections. The other hard section for me was 6.6- An Application to Treaty Verification. I don't quite know what all is going on there.