The basic problems We saw in Chapter 5 that the one-time pad is a cryptosystem that provides perfect secrecy, so why not use it? The obvious reason is that the key needs to be as long as the message and the users need to decide on this secret key in advance using a secure channel. Having introduced public key cryptography in Chapter 7 one might wonder why anyone would want to use a symmetric cryptosystem. Why not simply use RSA or some other public key cryptosystem and dispense with the need to exchange secret keys once and for all? The problem with this approach is that symmetric cryptosystems are generally much faster. For example in 1996, DES was around 1000 times faster than RSA. In situations where a large amount of data needs to be encrypted quickly or the users are computationally limited, symmetric cryptosystems still play an important role. A major problem they face is how to agree a common secret key to enable communications to begin. This basic ‘key exchange problem’ becomes ever more severe as communication networks grow in size and more and more users wish to communicate securely. Indeed while one could imagine. Alice and Bob finding a way to exchange a secret key securely the same may not be true if you have a network with 1000 users.
The basic problems We saw in Chapter 5 that the one-time pad is a cryptosystem that provides perfect secrecy, so why not use it? The obvious reason is that the key needs to be as long as the message and the users need to decide on this secret key in advance using a secure channel. Having introduced public key cryptography in Chapter 7 one might wonder why anyone would want to use a symmetric cryptosystem. Why not simply use RSA or some other public key cryptosystem and dispense with the need to exchange secret keys once and for all? The problem with this approach is that symmetric cryptosystems are generally much faster. For example in 1996, DES was around 1000 times faster than RSA. In situations where a large amount of data needs to be encrypted quickly or the users are computationally limited, symmetric cryptosystems still play an important role. A major problem they face is how to agree a common secret key to enable communications to begin. This basic ‘key exchange problem’ becomes ever more severe as communication networks grow in size and more and more users wish to communicate securely. Indeed while one could imagine. Alice and Bob finding a way to exchange a secret key securely the same may not be true if you have a network with 1000 users.
In this section, I wish to put quantum key distribution (QKD) in the wider context of a cryptosystem. I shall discuss informally some aspects that are considered important. The questions I wish to answer here are: “What are the ingredients needed to make a QKD-based cryptosystem work? What services does it bring? What are its limitations?” As I shall detail below, QKD may be used to provide the users with confidential communications. This can be achieved when we combine QKD and the one-time pad. For the quantum modulation, QKD needs a source of truly random numbers. Also, QKD requires a classical authenticated channel to work, so authentication plays an essential role. As a consequence, QKD must start with a secret key, making it a secret-key encryption scheme. I will also discuss what happens if classical cryptography is introduced in the system. Finally, I will describe the implementation of a simple cryptosystem on top of QKD. A key distribution scheme The first function of QKD is to distribute a secret key between two parties. The use of this key is outside the scope of this first section – the need for a secret key is omnipresent in cryptography. As depicted in Fig. 5.1, QKD relies on a classical authenticated channel for sifting and secret-key distillation and on random bits for the modulation of quantum states. The key produced by QKD can be intended for encryption purposes – this will be discussed in Section 5.2 – but is also required by authentication. A part of the distributed key is used for authentication. When QKD is run for the first time, however, an initial secret key must be used instead.
Currently many symmetric key cryptographic tools which are known to be quantum-safe. They all share Secret symmetric keys through an untrusted medium which is usually done with public key methods which are prone to quantum attacks. One among the recommended solutions to the key distribution problem is Quantum Key Distribution (QKD). QKD utilizes an authenticated Communication channel along with a quantum communication channel so that a secret key is generated. Whatever may be the protocol to implement proposed QKD, they all need both a quantum channel, and an authenticated classical. OTP (One Time Pad) is used when two parties wish to communications have to share a key called pad. This pad is a randomly generated key and the length of the key should be equal to the message so it can be sent. The proposed QKD parameters that result in almost 35.67% smaller keys for quantum security and an implementation of QKD in network which is publicly available and usable in practice.
Broadly speaking, cryptography is the problem of doing communication or computation involving two or more parties who may not trust one another. The best known cryptographic problem is the transmission of secret messages. Suppose wish to communicate in secret. For example, you may wish to give your credit card number to a merchant in exchange for goods, hopefully without any malevolent third party intercepting your credit card number. The way this is done is to use a cryptographic protocol. The most important distinction is between private key cryptosystems and public key cryptosystems.
Cryptographic protocols can be classified by the type of security against eavesdropping which they provide. There exist mathematically secure schemes whose security relies on mathematical proofs (like the Vernam cipher discussed below) or conjectures (like public key RSA encryption) about the complexity of deciphering the message without possessing the correct key. The majority of current secure public Internet connections rely on such schemes. Alternatively, a cryptographic setup may provide a physically secure method for communicating. In these setups the security is provided by the physical laws governing the communication protocol. Here we first discuss a provably secure classical communication protocol and then quantum methods for distributing the necessary keys. The BB84 protocol relies on the impossibility of perfectly distinguishing non-orthogonal quantum states from one copy of the quantum system. The scheme was invented in 1984 and is the first of its kind. In contrast, the Ekert91 protocol makes use of Bell correlations between entangled pairs of photons. These correlations are destroyed when Eve attempts to make a measurement on one of the particles but also when imperfections, such as decoherence processes, affect the scheme. As long as no such “elements of reality” are introduced, and Bell correlations violating local realism can be generated by Alice and Bob, no eavesdropper can be present. One-time pads and the Vernam cipher The Vernam cipher is a cryptographic protocol which allows the encryption and decryption protocol to be publicly known. The security of the protocol relies entirely on the key which is private and not publicly known. Alice and Bob share identical n -bit secret key strings (one-time pad).
According to modern cybersecurity, the concept of public key cryptography or asymmetric cryptography is one of the basics. Public key cryptography uses two keys: A private key is kept in secret and a public key is distributed publicly. Traditionally, symmetric cryptography uses a single key for everything from encryption to decoding, while quantum methods operate differently. Digital signatures, key exchange data channels, and even secure communication have been made possible thanks to the paradigm shift in cryptography. This chapter highlights the emergence of the rudimentary concepts, computational rules, and relevant advantages of using public key cryptography. It is paramount that this technology is deployed to ensure the integrity, confidentiality, and authenticity of digital communications.
The practical implementation of quantum information technologies requires, for the most part, highly advanced and currently experimental procedures. One exception is quantum cryptography, or quantum key distribution, which has been successfully demonstrated in many laboratories and has reached an advanced level of development. It will probably become the first commercial application of quantum information. In quantum key distribution, Alice and Bob exploit a quantum channel to create a secret shared key comprising a random string of binary digits. This key can then be used to protect a subsequent communication between them. The principal idea is that the secrecy of the key distribution is ensured by the laws of quantum physics. Proving security for practical communication systems is a challenging problem and requires techniques that are beyond the scope of this book. At a fundamental level, however, the ideas are simple and may readily be understood with the knowledge we have already acquired. Quantum cryptography is the latest idea in the long history of secure (and not so secure) communications and, if it is to develop, it will have to compete with existing technologies. For this reason we begin with a brief survey of the history and current state of the art in secure communications before turning to the possibilities offered by quantum communications. The history of cryptography is a long and fascinating one. As a consequence of the success or, more spectacularly, the failure of ciphers, wars have been fought, battles decided, kingdoms won, and heads lost. In the information age, ciphers and cryptosystems have become part of everyday life; we use them to protect our computers, to shop over the Internet, and to access our money via an ATM (automated teller machine). One of the oldest and simplest of all ciphers is the transposition or Caesarean cipher (attributed to Julius Caesar), in which the letters are shifted by a known (and secret) number of places in the alphabet. If the shift is 1, for example, then A is enciphered as B, B→C, · · ·, Y→Z, Z→A. A shift of five places leads us to make the replacements A→F, B→G, · · ·, Y→D, Z→E.