Number theory for computing

In 1977 three researchers at MIT, Ron Rivest, Adi Shamir and Leonard Adleman, found a way to let anyone encrypt a message that only one person could decrypt. Their paper appeared in Communications of the ACM in February 1978, and the scheme took their initials: RSA.

Every step of RSA is number theory you can do by hand: a greatest common divisor, a modular inverse, a power reduced modulo n. The oldest of those tools, the algorithm for the greatest common divisor, is in Book VII of Euclid's Elements, written more than two thousand years earlier.