ar X iv : 0 90 9 . 13 88 v 1 [ cs . C R ] 8 S ep 2 00 9 On the Relations Between Diffie - Hellman and ID - Based Key Agreement from Pairings ∗

This paper studies the relationships between the traditional Diffie-Hellman key agreement protocol and the identity-based (ID-based) key agreement protocol from pairings. For the Sakai-Ohgishi-Kasahara (SOK) ID-based key construction, we show that identical to the Diffie-Hellman protocol, the SOK key agreement protocol also has three variants, namely ephemeral, semi-static and static versions. Upon this, we build solid relations between authenticated Diffie-Hellman (Auth-DH) protocols and ID-based authenticated key agreement (IB-AK) protocols, whereby we present two substitution rules for this two types of protocols. The rules enable a conversion between the two types of protocols. In particular, we obtain the real ID-based version of the well-known MQV (and HMQV) protocol. Similarly, for the Sakai-Kasahara (SK) key construction, we show that the key transport protocol underlining the SK ID-based encryption scheme (which we call the “SK protocol”) has its non-ID counterpart, namely the Hughes protocol. Based on this observation, we establish relations between corresponding ID-based and non-ID-based protocols. In particular, we propose a highly enhanced version of the McCullagh-Barreto protocol.