In 2002

Boneh and Silverberg presented theory of multilinear forms and a multi-party Diffe-Hellman key agreement protocol using multilinear forms.H.K.Lee et al adopted certificates to authenticate group members and protect against middle-man attacks in this protocol.Subsequently

H.M.Lee et al deployed ID-base public keys other than certificates in the MAK protocol

and presented the ID-MAK protocol.Owing to simplicity of ID-base public keys

the ID-MAK Protocol is more efficient.In this paper

we analyze the security of the ID-MAK protocol

and have found that the ID-MAK protocol doesn’t really authenticate group members as claimed.Thus it cannot resist active attacks

and an adversary can pretend to be a legal member to obtain the group key.Based on the computational multilinear Diffe-Hellman assumption

we present two improved schemes to the ID-MAK protocol to remove this security defect.Both our improved protocols need only one round agreement.They support dynamic member change and key refresh.Our security analysis shows that they are secure.