Section 19.3 - 19.4

I wonder if Shor's algorithm could changed to somehow work on modern multi processor machines. The need for measuring frequencies scares me though it seems like a lot more opportunities for errors.

Section 19.1 - 19.2

Wow this stuff is weird. The issue of a practical implementation of the basis strikes be as a problem. Also the error issues involved with eavesdropping make it nice for crypto but impractical for implementing other computer components were signals are usually monitored and split up a lot. Qubit are pretty cool though, I can see how they provide more powerful computation in the long run.

Section 74 - 7.5

I don't see the point of the beta requirements for the Decisional Diffie Hellman Problem. Also I get the feeling that Diffie Hellman and Discrete Log should be equivalent but I guess since there is no proof then it could be so otherwise too. The DDH <=> El Gamal and CDH <=> El Gamal proofs are pretty nice, they remind be of a lot of Comp Sci proofs from my algorithms class.

Section 7.1 - 7.3

Baby step/Giant Step is a pretty cool application of divide and conquer find discrete logs I think is a cute solution. Index calculus on the other hand works but I don't quite see how to come up with the relationships it looks for. Also bit commitment is useless if there was a trusted third party then alice and bob could rely on the third party.

Section 6.6 - 6.7

Hurray for public keys, its extremely useful!! Its just nice to see how easily that RSA fits into the concept of public keys. The only weird thing in this section was trapdoor stuff. Coming up with things that have trapdoors or checking if something doesn't have a trapdoor is probably extremely difficult.

Section 6.5

Its a shame that they didn't come up with a way to avoid the creation of repetitions when calculating the congruence relations. I wonder what percentage of six hundred people's calculations had repetitions that would've been a total waste. Also the reasoning for using two large primes and the motivation for wanting to find the q squared relation was unclear to me. Why limit the scoope of the large primes?

Section 6.3 - 6.4

The Miller-Rabin Primality test is quite interesting, its a simple solution that could pretty easily be turned into a computer program. The quadratic sieve on the other hand really confuses me. I really don't see how the linear dependencies fit in. Well actually I can sort understand how it works, its just I could never imagine being able to come up with it on my own.