Provably secure group key agreement protocol based on ECDH with integrated signature

Abstract

This paper proposes a new two round authenticated contributory group key agreement (ACGKA) protocol based on elliptic curve Diffie-Hellman (ECDH) with integrated signature. In this technique, one node is picked up as the group controller, and this node runs an authenticated ECDH with the rest of the nodes to generate an authenticated shared key per each twoparty. It then merges these keys in another round in such a way that every member obtains the identical authenticated group key. Further, ACGKA is extended to dynamic ACGKA protocol. The dynamic ACGKA, being elliptic curve decisional Diffie Hellman-based, is less expensive and well suited for resource constrained networks such as mobile ad-hoc networks, and wireless sensor network. Also, we demonstrate that all the protocols proposed in this paper are provably secure in the standard model under ECDDH assumption and moreover secure against most of the active and passive attacks. Finally, the proposed protocol is compared with other prevalent ECDH and Diffie Hellman based group key agreement protocols, and results are found to be satisfactory. The simplicity and the elegance of the two-party D-H key agreement [13] motivated many researcher to extend D-H to group settings. Most of the GKA protocols are discrete logarithm problem (DLP) based. However, larger key lengths and heavier computational loads are very much critical for ad-hoc networks. The logical solution to this end is to employ elliptic curve cryptography [14,15], because it can provide high security with smaller key sizes, lesser computational expenses, and greater efficiency. In view of the aforementioned qualities elliptic curve discrete logarithm problem (ECDLP) based key agreement protocols are a natural solution to resource constrained networks such as mobile ad-hoc networks (MANETS) and wireless secure network (WSN). Apart from authentication, the dynamic nature of the protocol, namely, refreshing of GK as soon as members join and/or leave the group is now an integral part of several of these protocol investigations as else the

A provably secure cluster-based hybrid hierarchical group key agreement for large wireless ad hoc networks

“…Two-party DH-key agreement [34] is the origin for enormous amount of consequent GKA schemes. The majority of distributed/contributory-GKA protocols rely on generalizations of 2-party DH or its extensions [3,7,16,[35][36][37][38][39]. Key management in distributed/contributory-GKA are less difficult to deal with in each subgroup/cluster compared to the whole ad hoc network.…”

“…The management techniques for computational overheads must be considered into account. As ECDH is lightweight and efficient when compared to regular DH, the ECCbase [15] is used to secure dynamic authenticated GKAs: Consequently, in this paper an ECC-based NM-GKA [16] is used as a pre-requisite for the proposed protocol.…”

“…The proposed work has adopted hybrid based symmetric encryption where it combines the key distribution and key agreement. A digital signature scheme as in [16] can be used to authenticate our protocols. In view of the MANET's (Mobile Adhoc Network) dynamic, the proposed protocols adeptly address the dynamic events.…”

“…In contrast, usage and implementation of NM-GKA [16] protocol among all the nodes in the system may not be feasible for large WANETs. Consequently, we plan to use the same for each cluster and then for all the CHs in two levels hierarchically.…”

Provable secure lightweight hyper elliptic curve‐based communication system for wireless sensor networks

“…Lemma For any adversary 𝒜 who is computationally unbounded, the following holds: Prob [( T , sk 0 ) ← Fake ; sk 1 ← G ; b ← { 0 , 1 } :𝒜 ( T , sk b ) = b ] = 1/2 .Proof This lemma is to deal with the Test query, the proof of which follows from the fact that in Fake the session key sk is completely independent of the transcript T generated there and Using the same techniques as in lemma 2 of Naresh . ◻…”