A DH-based key exchange protocol for wireless mobile networks was proposed by Park: The system has a

A DH-based key exchange protocol for wireless mobile networks was proposed by Park: The system has a common prime modulus p and a generator g. Each party i has a long-term private key xi ? Zp-1 and a public key Xi = g xi (mod p). To establish a session key between a mobile subscriber M and a base station B, the following protocol is executed (with all arithmetic in Zp): 1. B ? M : g xB+NB 2. M ? B : NM + xM where NB and NM are one-time random nonces (once used random numbers). B calculates the session key as KMB = (g xM+NM X -1 M ) NB and M calculates it as KMB = (g xB+NB X -1 B ) NM Then they complete the authentication with a challenge-response using this KMB. 1. Show that the Park’s protocol is correct in the sense that B and M calculate the same KMB value.