9 - Cryptography

Summary

We dance round in a ring and suppose, But the Secret sits in the middle and knows.

Robert Frost, The Secret Sits (1942)

In this chapter we explore the merging of quantum computation and classical cryptography. This is a new and exciting field of pure and applied research known as quantum cryptography.

We begin with the basics of classical cryptography in Section 9.1. Section 9.2 demonstrates a quantum cryptographic protocol that uses two different bases. We improve on this in Section 9.3, where a protocol with one basis is employed. Section 9.4 shows how to use entanglement to secretly send a message. We conclude with Section 9.5, in which teleportation is demonstrated.

CLASSICAL CRYPTOGRAPHY

Before delving into quantum cryptography, we need to familiarize ourselves with the core ideas of classical cryptography. A good place to start is the following definition.

Definition 9.1.1 Cryptographyis the art of concealing messages.

Indeed, this is precisely what the etymology reveals: “Cryptography” is a compound of two Greek words, crypton and graphein, which mean, respectively, hidden and writing.

Turning an ordinary message into an indecipherable one is called encryption. The opposite action, i.e., restoring the original message, is decryption. The original message is generally referred to as the plaintext, and the encrypted message is the ciphertext. A method for encryption is often referred to as an encryption protocol.