Democratic societies depend on trust in elections and their results. Throughout the 2016 presidential election, and since President Trump’s inauguration, allegations of Russian involvement in the U.S. presidential campaign have raised concerns about how vulnerable American elections are to hacking or other types of interference. Various investigations – involving congressional committees, the FBI and the intelligence community – are underway, seeking to understand what happened and how. There are many potential problems with elections: Voters can be individually coerced or bribed into changing their votes; the public can be misled about important facts, causing them to draw inaccurate conclusions that affect their votes; and the physical – and electronic – process of voting can itself be hacked. Without conducting a full, vote-by-vote manual recount, which is impossible because many voting machines leave no paper trail, how can we be sure an election was conducted fairly and not interfered with?