It is said that IPSEC may not work with Network Address Translation (NAT) (RFC 1631). However, whether IPSEC will work with NAT depends on which mode of IPSEC and NAT we use. Suppose we use true NAT, where only IP addresses are translated (without port translation). Will IPSEC and NAT work in each of the following cases? Explain why or why not
(a) IPSEC uses AH transport mode.
(b) IPSEC uses AH tunnel mode.
(c) IPSEC uses ESP transport mode.
(d) IPSEC uses ESP tunnel mode.
(e) What if we use PAT (Port Address Translation), also known as Network Address/Port Translation (NAPT) in NAT, where in addition to IP addresses, port numbers will be translated to share one IP address from outside the private networ?