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On batch verification with group testing for vehicular communications

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Abstract

In this paper, an efficient identity-based batch signature verification scheme is proposed for vehicular communications. With the proposed scheme, vehicles can verify a batch of signatures once instead of in a one-by-one manner. Hence the message verification speed can be tremendously increased. To identify invalid signatures in a batch of signatures, this paper adopts group testing technique, which can find the invalid signatures with few number of batch verifications. In addition, a trust authority in our scheme is capable of tracing a vehicle’s real identity from its pseudo identity, and therefore conditional privacy preserving can also be achieved. Moreover, since identity-based cryptography is employed in the scheme to generate private keys for pseudo identities, certificates are not required and thus transmission overhead can be significantly reduced.

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Notes

  1. Note that with the IBV scheme, in order to get a short signature, we use an MNT curve [41] with 160-bit q, where the bilinear map \({\hat{e} : {\mathbb{G}}_1 \times {\mathbb{G}}_2 \rightarrow {\mathbb{G}}_T}\) is asymmetric, \({{\mathbb{G}}_1 \neq {\mathbb{G}}_2}\), and elements in \({{\mathbb{G}}_1}\) are 161 bits long.

  2. With the IBV scheme, each message sent by a vehicle corresponds to a distinct identity. Thus, to achieve the same privacy level as the IBV’s, the vehicle using the public key based schemes also needs to change an identity for each sending message. That is the reason why verification time for ECDSA and BLS should be doubled in this paper.

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Acknowledgments

The authors thank Prof. Xuemin (Sherman) Shen, Prof. Xiaodong Lin, and Rongxing Lu for providing valuable suggestions and discussions on this paper. The research is financially supported by Natural Sciences and Engineering Research Council of Canada (NSERC).

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada

    Chenxi Zhang & Pin-Han Ho

  2. Department of Telecommunications and Media Informatics, Budapest University of Technology and Economics, Magyar tudosok krt. 2, H-1117, Budapest, Hungary

    Janos Tapolcai

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  1. Chenxi Zhang
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Correspondence to Chenxi Zhang.

Additional information

Part of this paper was presented in Infocom 2008 [1].

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Zhang, C., Ho, PH. & Tapolcai, J. On batch verification with group testing for vehicular communications. Wireless Netw 17, 1851–1865 (2011). https://doi.org/10.1007/s11276-011-0383-2

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