On the Relations Between Diffie-Hellman and ID-Based Key Agreement from Pairings

TL;DR

This paper explores the connections between Diffie-Hellman and ID-based key agreement protocols from pairings, introducing conversion rules and deriving ID-based variants of well-known protocols like MQV and HMQV.

Contribution

It establishes formal relations and conversion rules between Diffie-Hellman and ID-based protocols, and derives ID-based versions of MQV, HMQV, and McCullagh-Barreto protocols.

Findings

ID-based protocols have variants similar to Diffie-Hellman

Conversion rules enable transforming protocols between types

Derived ID-based MQV, HMQV, and enhanced McCullagh-Barreto protocols

Abstract

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 \emph{ephemeral}, \emph{semi-static} and \emph{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 \emph{substitution rules} for this two types of protocols. The rules enable a conversion between the two types of protocols. In particular, we obtain the \emph{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.