(Difficult) I am having a hard time understanding what has functions are used for. I know the lecture mentioned using them for digital signatures, and error checking, but there really is no decryption involved, right? Everything we have dealt with so far has had an inverse function, even in the case of RSA where the inverse is difficult to find without the prime p and q, there still existed an inverse function of some sort. Are there hash functions with no inverse function at all?
(Reflective) I found the data integrity application of hash functions to be quite interesting. This is a clever way to prevent Eve from modifying a message en route to Bob. I was curious though, one thing Eve could do is create her own message, run it through the hash function (if she knows the function), and send m and H(m). Are hash functions used in conjunction with other cryptographic systems? It seems there would be some other method needed to verify who the message was sent from. I understand we are just introducing hash functions now, but I hope at some time in the class we will have a chance to see how various cryptosystems might be used together in a real-world application.
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