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comment How to Compute C^2 in AES MixColumns Matrix?
Good answer. One minor quibble with the statement "the character of K": the correct mathematical term is characteristic. See: en.wikipedia.org/wiki/Characteristic_(algebra).
comment Recommended skills for a job in cryptology
@Zvpunry It's probably way too late for me to respond to this, but I just saw your comment. Learning Python and Sage is pretty cool, but as you said, it won't be of much usefulness to the crypto engineering problem. There are plenty of available programming jobs that will take a math undergrad with good Python programming skills though. So, you may just want to start from there. If you're truly interested in the hardware aspects of things though, that's a sufficiently different topic that you may want to take some EE classes before you leave college, so as to be better prepared.
comment Can we proxy-re-encrypt using homomorphic encryption schemes?
@sashank Yes, Gentry did that because the usual semantic security guarantee of encryption schemes has a sneaky loophole: it's not at all clear what happens when you encrypt a secret key. As a simple example, think about what happens with a one-time-pad when it's used to encrypt a secret key under itself; it's easy for an attacker to be able to detect when this has happened, even though encryption is supposed to "hide everything" about a message. To learn more about this topic, try Googling for "circular security" or "key-dependent message."