This work presents an overview of security challenges associated with Automated Driving Systems (ADSs), covering on- and off-board computations, trustworthiness of data sources, and communications. We focus on the security of computations and emergent involvement of the edge computing paradigm in ADSs. Analysis of ADS and edge computing security reveals that ensuring the integrity of offloaded computations and availability of the offloading service are major security challenges that must be addressed if edge computing is to play a significant role in ADSs. Verifiable computation is investigated as a security solution to ensure integrity of offloaded ADS computations, and a method for deciding on the adequateness of a verifiable computation scheme for ADS applications is proposed.