Invalid Signatures Searching Bitwise Divisions-Based Algorithm for Vehicular Ad-Hoc Networks

Abstract

Vehicular ad-hoc networks (VANETs) are the crucial part of intelligent transportation systems (ITS), which are brought to enhance the security, efficiency, and comfort of transportation. VANETs have aroused extensive attention in the world recently. One of the challenges in practice is real time and low delay, which strongly requires VANETs to be efficient. Existing schemes have properly solved the problem which is how to aggregate the signatures and verify the aggregated signature. However, few solutions are proposed to pinpoint all invalid signatures if existing. The algorithms that can find all invalid signatures are not efficient enough. Following consideration of the above deficiencies of existing approaches, this paper proposes a factorial bitwise divisions (FBD) algorithm and its optimized version and early-stopping factorial bitwise divisions (EFBD) algorithm. Both algorithms are parallel-friendly. Compared with the binary-based batch verification algorithm, the experimental results demonstrate that the proposed algorithms achieve better performance in both theory and practice at low invalid signatures’ rate. Especially, in the parallel condition, when the number of invalid signatures is 1, the proposed algorithms cost only one aggregation-verification delay, while the comparison is more than ${\log }_{2}n$ times.