Abstract: Recently,many different anonymous authentication schemes have been proposed for privacy protection of vehicles in vehicular ad hoc networks (VANETs).In 2018,Vijayakumar et al.proposed a computationally efficient privacy preserving anonymous authentication scheme for VANETs (CPAV) and anonymous batch authentication scheme for VANETs (ABV).The schemes can achieve anonymous mutual authentication between the vehicle and the road side unit(RSU),as well as anonymous batch authentication of vehicle by the RSU,and resist bogus attacks,forgery attack,and associated attacks.TA (Trusted Agency) can track the true identity of registered vehicles when necessary.This paper deeply analyzed the security of CPAV and ABV.In CPAV scheme,the external attackers are fully able to successfully conduct bogus attack and forgery attack,which proves that this scheme does not satisfy non-repudiation,nor can it conduct conditional tracking for vehicles.In addition,because the anonymous identity used in the scheme is unique,the scheme cannot resist the associated attacks,which indicates that this scheme doesn’t possess the so-calledunlinkability.At last,it’s also proved that the anonymous batch authentication (ABV) scheme can’t resist forgery attack.

Key words: Anonymous authentication, Associated attack, Bogus attack, Conditional tracking, Forgery attack, Privacy preserving, Vehicular ad hoc networks (VANETs)