In IKE Phase 1 digital signature main mode, proof^ and proofg are signed by Alice and Bob, respectively. However, in IKE Phase 1, public key encryption main mode, proof^ and proofB are neither signed...

In IKE Phase 1 digital signature main mode, proof^ and proofg are signed by Alice and Bob, respectively. However, in IKE Phase 1, public key encryption main mode, proof^ and proofB are neither signed nor encrypted with public keys. Why is it necessary to sign these values in digital signature mode, yet it is not necessary to public key encrypt (or sign) them in public key encryption mode?