7.3-7.5

1. I think the real question here is, if Bob is smart enough to understand that there is a unique solution to the equation B=a^x (mod p) and that it encapsulates the information he is interested in, why would he believe that Alice had a system predicting the outcomes of football games?

2. In a lot of fields, it seems like there is a meet-in-the-middle of utility vs. theory or maybe practicality vs. theory. Even more general, there are people at opposing sides of some spectrum who are trying to solve problems almost solely with the tools they have. For instance, in computing, since faster is better, both hardware people and software people work to make their component of the system faster. Since their improvements are independent of the others', an even greater speedup is achieved. So it is with mathematics, it seems to me. We have applied mathematicians who have outlined a set of properties a given cryptographic system must have, and some pure mathematician who has invested a lot in some family of problems and understands the difficulties provides a solution. This in turn causes more research to be done in this class of problems (perhaps by people with ill intentions), and free enterprise improves humanity once again.