Efficient self-healing group key distribution with revocation capability

Abstract

This paper presents group key distribution techniques for large and dynamic groups over unreliable channels. The techniques proposed here are based on the self-healing key distribution methods (with revocation capability) recently developed by Staddon et al. [27]. By introducing a novel personal key distribution technique, this paper reduces (1) the communication overhead of personal key share distribution from O(t 2 log q) to O(t log q), (2) the communication overhead of self-healing key distribution with t-revocation capability from O((mt 2 + tm) log q) to O(mt log q), and (3) the storage overhead of the self-healing key distribution with t-revocation capability at each group member from O(m 2 log q) to O(m log q), where t is the maximum number of colluding group members, m is the number of sessions, and q is a prime number that is large enough to accommodate a cryptographic key. All these results are achieved without sacrificing the unconditional security of key distribution. In addition, this paper presents two techniques that allow trade-off between the broadcast size and the recoverability of lost session keys. These two methods further reduce the broadcast message size in situations where there are frequent but short-term disruptions of communication and where there are long-term but infrequent disruptions of communication, respectively.

Wireless broadcast encryption based on smart cards

“…Typical examples include Naor-Pinkas schemes [26], Kogan et al's schemes [18] and Liu et al's schemes [21]. The Naor-Pinkas scheme for single revocation can revoke i (BN) users per revocation, where N is the maximum number of revoked users.…”

“…Kogan et al's scheme with the triangular construction can revoke up to i Á N=T (where T is the total number of revocations) users in the ith revocation, and the overall number of revoked users is N. Kogan et al's scheme with the rectangular construction allows to revoke up to N users in one revocation, and the overall number of revoked users is still upper-bounded at N. These schemes need to re-card all smart cards after up to N users are revoked. Based on selfhealing group key distribution (with revocation capability) developed in [29], Liu et al proposed a scheme to allow users who do not receive a particular session key via the key distribution broadcast to recover the session key on their own in [21]. Although the Liu et al scheme was proposed for self-healing group key distribution, it can be simplified to distribute broadcast keys to a set of privileged users as we show at the beginning of Sect.…”

“…If (21) holds, most likely, the attacker has found K 0 ða j Þ successfully. The probability of success in finding K 0 ða j Þ is Wireless Netw (2010) 16:153-165 159 about jR t j=p kþ1 ; where k is the number of randomly chosen k i .…”

“…Although the Liu-Ning-Sun scheme [21] was proposed for self-healing group key distribution, it can be simplified to distribute broadcast keys to a set of privileged users as follows. In order to revoke users R 0…”

“…A few such schemes already exist, such as Naor-Pinkas schemes [26], Kogan et al's schemes [18], and Liu et al's schemes [21]. Recently, some schemes based on pairing were proposed, such as [9][10][11].…”