(Difficult) I understand that we may learn more about this in another section later in the book, but the lecture briefly mentioned the differences of the ElGamal and RSA system signature scheme. The RSA is a message recovery scheme, and ElGamal is not? Why is it harder to retrieve the message m from the ElGamal system?
(Reflective) In the section talked about signing the hash of a message, I started thinking about the pros and cons of sign a hash as opposed to signing the original message. In most cases, a hash will be shorter, and thus is faster to sign. However, if hash functions are too small, they are more susceptible to brute force attacks. Is there a common size limit for hash functions today? Has this size limit changed over the years as technology and techniques have developed? How does the probability of finding two messages with the same hash function change if the messages are of a fixed length, or arbitrary long?
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