In this letter, we improve NF'07 (Nakanishi and Funabiki) VLR group signature scheme such that it satisfies exculpability and has lower computation costs. In the proposed scheme, a group member generates his own private key together with the group manager in order to realize exculpability while the signature size is not made longer. Also, a new revocation check method is proposed at the step of verifying, and the computation costs of verifying are independent of the number of the revoked members, while they are linear with the number of the revoked members in the original scheme. Thus, the proposed scheme is more efficient than the original scheme and can be applicable to mobile environments such as IEEE 802.1x.

To solve the problems of the existing trusted network access protocols for Wireless Local Area Network (WLAN) mesh networks, we propose a new trusted network access protocol for WLAN mesh networks, which is abbreviated as WMN-TNAP. This protocol implements mutual user authentication and Platform-Authentication between the supplicant and Mesh Authenticator (MA), and between the supplicant and Authentication Server (AS) of a WLAN mesh network, establishes the key management system for the WLAN mesh network, and effectively prevents the platform configuration information of the supplicant, MA and AS from leaking out. Moreover, this protocol is proved secure based on the extended Strand Space Model (SSM) for trusted network access protocols.

Trusted network access protocols are proposed for the security and authorization of network-access requests. Because they differ greatly from traditional security protocols on security demands, they can not be analyzed with previous strand space works directly. To solve this problem, we first give some extensions necessary to verify them in this letter. Moreover, we point out Zhuo Ma et al.'s MN-TAP protocol is unsecure based on the Strand Space Model (SSM), and then improve the MN-TAP protocol and show that the improved MN-TAP protocol is secure in the SSM.