Public keys can be broadcast all over the world, only the private keys have to be kept secret.
The RSA algorithm is currently the most popular example of such a system. When divided by 15 this gives a quotient of 572662306 and a remainder of 2, as predicted by Euler's theorem. We obtain the same remainder of 12. Suppose Bob wants Alice to send him a secret message. Bob begins by randomly choosing two large primes p and q.