Election Security Assistance Act This bill addresses security threats to federal elections. Specifically, the bill requires the Department of Homeland Security (DHS) and the Office of the Director of National Intelligence to jointly report on foreign threats to elections in the United States, including physical and cybersecurity threats. This annual report must be submitted to Congress and chief state election officials. Additionally, the bill requires the Cybersecurity and Infrastructure Security Agency and the Election Assistance Commission (EAC) to jointly establish a voluntary process to test for and monitor covered voting systems for cybersecurity vulnerabilities. The EAC must also establish a process to provide for the deployment of appropriate labeling available through the EAC's website to indicate that covered voting systems passed the most recent cybersecurity testing. The bill requires federal entities to share information with DHS regarding election cybersecurity incidents. The bill also requires DHS to share information with state and local officials regarding election cybersecurity incidents.