Cs 7880 Graduate Cryptography Lecture 2: Macs, Statistical Distance, Statistical Security

The MAC construction that we saw in the previous lecture was not very practical in the sense that we can improve the construction by using the same key and tag length as before but for a bigger message space. That is, for some prime p we have: • K = Zp × Zp • M = Zp for some d ≥ 1 • T = Zp (We can replace Zp by any finite field F. In particular, it’s useful to use a binary extension field F2` since in that case keys and messages are just bit string of length `.). For a key k = (x, y) and message m = (m1, . . . ,md) we define