ates 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. Here, the discussion is expanded to qualify the difficulty of the factorization problem by classical computing means, with a detailed analysis of the time and memory requirements, yielding predictions for solving the various RSA challenges. I then briefly describe DES with its double- and triple- implementation variants (2DES, 3DES), and the innovative features of the advanced encryption standard (AES). Then follows a discussion of the other applications of modern cryptography, including signature and authentication, which are based on the principle of one-way encryption or hashing. I then move to quantum cryptography, which is now placed in the global context of communication security, rather than addressed as a separate field. Quantum cryptography is widely believed to provide "provably secure" means to exchange information, based on fundamental quantum-mechanics principles. This is the introductory concept of secure communication channel. As we shall see in this chapter, the concept boils down to that of quantum key distribution (QKD), solving the age-long issue of key exchange, without interception risks, as an absolute, "quantum" competitor to PKC-RSA. I then describe the three hero protocols, referred to as BB84, B92, and EPR protocols for QKD. As it turns out, and contrary to widespread belief, none of Classical and quantum cryptography these protocols is provably safe unless extra security steps are implemented. Indeed, classical-coding means, "esoterically" referred to as information reconciliation, privacy amplification, or secret key dist