Public-key cryptography / asymmetric cryptography, creating a key pair. A big random number is used to create a key pair. When the keys have been made the big random number is thrown away. Without knowledge of the random number it should be "impossible" to create the private key from the public key. (In many algorithms it is also "impossible" to create the public key from the private key once the random number has been thrown away.) The public key can be freely published to the world.

Note that most key making functions internally need more than one random number. To handle this the "big random number" usually is fed as a seed to a cryptographically secure random number generator that then produces many pseudo random numbers for the key making function.

Original illustration by David Göthberg, Sweden.