Department of Mathematics
Mathematics in Science & Society
by
Daniel J. Bernstein

Cryptography---literally, ``secret writing''---uses secret, uniformly distributed random ``keys'' to mathematically protect information against espionage and sabotage. In this talk I'll explain the highlights of modern cryptography:

• It's easy to guarantee the secrecy and authenticity of a message if the sender and receiver share a long key. Unfortunately, long keys are expensive. Fortunately, the sender and receiver can use a short key instead: long keys are (conjecturally) computationally indistinguishable from suitable functions of short keys.
• The sender and receiver have to agree on a key without revealing the key to spies. One big surprise is that the sender and receiver can do this in public: they can exchange public messages and, from the public messages, extract a shared secret that (conjecturally) nobody else can determine.
• Another big surprise is that the receiver doesn't even need a key if he merely wants to check the integrity of a public message: the sender, and (conjecturally) nobody but the sender, can generate a public signature that anyone can verify.

Then I'll talk about some of the political and legal issues surrounding cryptography: in particular, how I ended up as the plaintiff in a lawsuit against the government; how the courts actually interpret the First Amendment; and the latest news from my case.