6.1, due on October 8

1. (Difficult) Actually understanding how to implement RSA doesn't seem all that hard.  If you take some of the assertions as given, then RSA seems pretty simple.  The difficulty comes in trying to understand why the math works the way it does.  For example, why multiplying by the decryption exponent works.  The claims involving finding ɸ(n) or d were somewhat hard to follow with light reading.  Perhaps more practice with Euler's theorem and class lecture will help.
2. (Reflective) I thought that showing that finding ɸ(n) or d is nearly the same as factoring n was interesting.  I wonder, though, if it has been proven that factoring n is hard?
   I wonder if we sometimes underestimate the value of public key cryptography.  I wonder if the Internet would be what it was today, if it wasn't as easy to establish secure connections between parties who previously hadn't known each other.  It seems online shopping, banking, etc. would be more difficult.  I wonder if the Internet would be as useful if there weren't these types of economic reasons to drive its development.  Perhaps some may argue that a less commercial Internet would be a good thing, but regardless it would be interesting to see how it would be different without public key cryptography.