The following authenticated key agreement protocol is given: 1 : A ? B : g x mod p 2 : B ? A : g y..

The following authenticated key agreement protocol is given: 1 : A ? B : g x mod p 2 : B ? A : g y mod p, Ek(SB(g y mod p, gxmodp)) 3 : A ? B : Ek(SA(g x mod p, gy mod p)) We assume that the parties have agreed on a (g, p) pair for Diffie-Hellman key exchange, that each user has RSA keys for digital signatures and that they have agreed on a block cipher E for use in subsequent encryption. Furthermore, k is the agreed secret key and SA and SB denotes A:s and B:s signature operations, respectively. Describe in details (as a list) A:s and B:s actions at receipt of messages 2 and 3 and what beliefs they have at that stage. Are A and B successfully authenticated to each other after protocol run ?