In this paper, several algorithms for batch verification of ECDSA signatures are studied. The first of these algorithms is based upon the naive idea of taking square roots in the underlying field. In order to improve the efficiency beyond what can be achieved by the naive algorithm, two new algorithms are proposed which replace square-root computations by symbolic manipulations. Experiments carried out on NIST prime curves demonstrate a maximum speedup of above six over individual verification if all the signatures in the batch belong to the same signer, and a maximum speedup of about two if the signatures in the batch belong to different signers, both achieved by a fast variant of the second symbolic-manipulation algorithm. In terms of security, all the studied algorithms are equivalent to standard ECDSA* batch verification. These algorithms are practical only for small (≤8) batch sizes. The algorithms are also ported to the NIST Koblitz curves defined over fields of characteristic
In this paper, we make a survey of the known schemes for V2V (vehicle to vehicle) and V2I (vehicle to infrastructure) authentication in VANETs (vehicular ad hoc networks). We consider a variety of safety applications in VANETs, identify authentication as one of the security requirements and discuss the security challenges for these applications. Existing authentication schemes based on digital signatures are discussed along with schemes based on hash chains and hash trees. It has also been shown how the level of security of these schemes is increased by the involvement of a trusted Certification Authority. We also focus on issues pertaining to anonymity, unlinkability, traceability and computation and communication overhead. Finally, we summarise the limitations of the existing authentication schemes in real-life applications and conclude that further research is essential in this area.
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