Conditional Privacy Preserving Authentication (CPPA) schemes are an effective way of securing communications in Vehicular Adhoc Networks (VANETs), as well as ensuring user privacy and accountability. Cryptanalysis plays a crucial role in pointing out the vulnerabilities in existing schemes to enable the development of more resilient ones. In 2019, Zhang proposed a CPPA scheme for VANET security (PA-CRT), based on identity batch verification (IBV) and Chinese remainder theorem (CRT). In 2023, this scheme was crypt-analyzed by Tao. In this paper we provide our own crypt analysis of Zhang’s scheme and propose counter measures to mitigate Tao’s attacks. Furthermore, in 2021, Xiong proposed a Certificateless Aggregate Signature (CLAS) scheme which was cryptanalyzed by Shim in 2023. Xiong subsequently proposed a modified CLAS scheme which is also cryptanalyzed in this paper.