“On the Internet, nobody knows you’re a dog.” The famous 1993 New Yorker cartoon (Wikipedia) was a joke—but it pointed at a real problem. How do you know you’re interacting with a real human online? Or a human of the right age, with the right credentials? Today that question is sharper than ever.

Threshold encryption is a foundational primitive for building distributed systems that need confidentiality without relying on any single party. A sender encrypts a message to a quorum of $n$ users such that any set of $t$ users can decrypt the ciphertext, while no set of $t-1$ users can. Importantly, the ciphertext can be succinct: it does not grow with $n$ (or $t$).