It should be clear from Chapter 6 that perfect secrecy is useful in encryption. However, the idea can be useful in constructing other cryptographic building blocks. In this chapter, we discuss two examples.

Secret-sharing and perfect secrecy

The idea of perfect secrecy can be used to cryptographically “split” a secret into two parts. Each part can be given to a different person. Either person on her own learns nothing about the secret by receiving her part; together the two people can reconstruct the secret.

Imagine, for example, that the bank president wants to give her two vice presidents the combination to the safe (in case the safe needs to be opened on a day the president is incommunicado), but wants them to have only joint access. She can use secret-sharing to split the combination between the two vice-presidents.

Let f (plain, key) be the encryption function for a perfectly secure cryptosystem. We will use this cryptosystem to split the secret. The choice of cryptosystem is not intended to be secret; we assume this choice is known to all. The choice of cryptosystem restricts the choice of secret to be shared; the secret must be one of the cryptosystem's possible plaintexts.