25 - Classical and quantum cryptography

Summary

This final chapter concerns cryptography, the principle of securing information against access or tampering by third parties. Classical cryptography refers to the manipulation of classical bits for this purpose, while quantum cryptography can be viewed as doing the same with qubits. I describe these two approaches in the same chapter, as in my view the field of cryptography should be understood as a whole and appreciated within such a broader framework, as opposed to focusing on the specific applications offered by the quantum approach. I, thus, begin by introducing the notions of message encryption, message decryption, and code breaking, the action of retrieving the message information contents without knowledge of the code's secret algorithm or secret key. I then consider the basic algorithms to achieve encryption and decryption with binary numbers, which leads to the early IBM concept of the Lucifer cryptosystem, which is the ancestor of the first data encryption standard (DES). The principle of double-key encryption, which alleviates the problem of key exchange, is first considered as an elegant solution but it is unsafe against code-breaking. Then the revolutionary principles of cryptography without key exchange and public-key cryptography (PKC) are considered, the latter also being known as RSA. The PKC–RSA cryptosystem is based on the extreme difficulty of factorizing large numbers. This is the reason for the description made earlier in Chapter 20 concerning Shor's factorization algorithm.