Law enforcement authorities across Europe and the U.S. shut dozens of illegal websites and arrested some operators, employing new and as yet unknown techniques to unmask those using an anonymity network.

Authorities said on Friday they made the arrests by piercing the anonymity offered by Tor, a network that relies on encryption tools and 1,000s of servers to mask online activities. Tor, which is partly funded by the U.S. government, is used by dissidents in authoritarian countries such as Iran, China and Saudi Arabia to access...