Generalized Self-healing Key Distribution Using Vector Space Access Structure

Abstract

We propose and analyze a generalized self-healing key distribution using vector space access structure in order to reach more flexible performance of the scheme. Our self-healing technique enables better performance gain over previous approaches in terms of storage, communication and computation complexity. We provide rigorous treatment of security of our scheme in an appropriate security framework and show it is computationally secure and achieves forward and backward secrecy. Keywords: key distribution, self-healing, wireless network, access structure, computational security, forward and backward secrecy. IntroductionSelf-healing key distribution deals with the problem of distributing session keys for secure communication to a dynamic group of users over an unreliable, lossy network in a manner that is resistant to packet lost and collusion attacks. The main concept of self-healing key distribution schemes is that users, in a large and dynamic group communication over an unreliable network, can recover lost session keys on their own, even if lost some previous key distribution messages, without requesting additional transmissions from the group manager. This reduces network traffic and risk of user exposure through traffic analysis and also decreases the work load on the group manager. The key idea of self-healing key distribution schemes is to broadcast information that is useful only for trusted members. Combined with its pre-distributed secrets, this broadcast information enables a trusted member to reconstruct a shared key. On the contrary, a revoked member is unable to infer useful information from the broadcast. The only requirement that a user must satisfy to recover the lost keys through self-healing, is its membership in the group both before and after the sessions in which the broadcast packet containing the key is sent. A user who has been off-line for some period is able to recover the lost session keys immediately after coming back on-line. Thus self-healing approach of key distribution is stateless.

An Efficient Self-Healing Key Distribution with Resistance to the Collusion Attack for Wireless Sensor Networks

“…In contrast to the family of the selfhealing key distribution schemes proposed in [5] and [10], our construction provides reduction in the storage overhead, which is one of the main improvement of our scheme over the previous work. Although some previous work based on shamir's secret sharing are more efficient than our scheme, as we have discussed before, these schemes have limitations, i.e., the maximum number of revoked users is constrained by the degree of the polynomial.…”

“…Our scheme reduces storage overhead over the previous approaches, resists collusion between the [6] t(m − j + 1) log q 1 2 t(m 2 − m + 2) log q No [10] (m − j + 1) log q (t + 1) log q No [11] (2m + 1) log q (t + 1) log q Yes Our scheme (m − j + 2) log q (t + 1 + j) log q Yes new joined users and the revoked users, and is scalable to very large groups in highly mobile, volatile, and hostile wireless network. Our scheme is analyzed in an appropriate security model to prove that it is computationally secure and achieves both forward and backward secrecy.…”

Generalized self-healing key distribution in wireless adhoc networks with trade-offs in user's pre-arranged life cycle and collusion resistance

“…Improvements in efficiency are obtained by relaxing the security slightly -from unconditional to computational [13,8,9,15]. The schemes [19,20,25,9] are based on vector space access structure instead of Shamir's [21] secret sharing.…”

“…Improvements in efficiency are obtained by relaxing the security slightly -from unconditional to computational [13,8,9,15]. The schemes [19,20,25,9] are based on vector space access structure instead of Shamir's [21] secret sharing. The hash chain based schemes [13,8,9,15] are computationally secure and are highly efficient compared to the existing unconditionally secure schemes.…”

“…The schemes [19,20,25,9] are based on vector space access structure instead of Shamir's [21] secret sharing. The hash chain based schemes [13,8,9,15] are computationally secure and are highly efficient compared to the existing unconditionally secure schemes. However, these hash chain based constructions have the fatal defect of not being collusion resistant in the sense that the collusion between new joined users and the revoked users are able to recover all the session keys which they are not entitled to.…”