Preface

Chapter 8 **The Concept of Mass Based on Accelerated Conservation of Energy within Asymmetric Space-Time Phases 153**

Chapter 9 **Quantum Calculus with the Notion δ±-Periodicity and Its**

Neslihan Nesliye Pelen, Ayşe Feza Güvenilir and Billur Kaymakçalan

Agaddin Khanlar Mamedov

**Applications 183**

**VI** Contents

One of the most effective ways to ensure confidentiality and data integrity during transmis‐ sion is cryptography. The purpose of the cryptographic system is to provide key distribu‐ tion, authentication, legitimate user authorization, and encryption. Today, key distribution is one of the most important problems of cryptography. This problem can be solved with the help of the following schemes: classical information-theoretic scheme, classical public-key cryptographic scheme, classical computationally secure symmetric-key cryptographic scheme, trusted courier key distribution, and quantum key distribution (QKD).

QKD includes the number of protocols (such as BB84, SARG04, E91, B92, six-state protocol, Goldenberg-Vaidman protocol, and Koashi-Imoto protocol), and the main task of these is en‐ cryption key generation and distribution between the two users connecting through quantum and classical channels. The main advantages of all QKD protocols are as follows: (1) these protocols always allow eavesdropping to be detected because eavesdropper's connection brings much more error level (compared with natural error level) to the quantum channel. The laws of quantum mechanics allow eavesdropping to be detected, and the dependence between error level and intercepted information to be set. This allows to apply the privacy amplifica‐ tion procedure that decreases the quantity of information about the key, which can be inter‐ cepted by eavesdropper. Thus, QKD protocols have an unconditional (information-theoretic) security. (2) The information-theoretic security of QKD allows using an absolutely secret key for further encryption using the well-known classical symmetrical algorithms. Thus, the entire information security level increases. It is also possible to synthesize QKD protocols with the Vernam cipher (one-time pad), which, in complex with unconditionally secured authenticated schemes, gives a totally secured system for transferring the information.

Besides, there are also disadvantages of QKD protocols that are as follows: (1) a system based only on QKD protocols cannot serve as a complete solution for key distribution in open networks because additional tools for authentication are needed. (2) The limitation of quantum channel length is caused by the fact that there is no possibility of amplification without quantum properties being lost. However, the technology of quantum repeaters could overcome this limitation in the near future. (3) There is a need for using the weak-co‐ herent pulses instead of single-photon pulses. This decreases the efficiency of protocol in practice. However, this technological limitation might be defeated in the near future. (4) The data-transfer rate decreases rapidly with an increase in the quantum channel length. (5) Pho‐ ton registration problem leads to a key rate of decrease in practice. (6) Photon depolarization in the quantum channel leads to errors during data transfer. Now, the typical error level equals a few percent, which is much greater than the error level in classical information and communication systems. (7) Difficulty in the practical realization of QKD protocols for *d*-lev‐ el (multilevel) quantum systems. (8) The high price of commercial QKD systems (more than \$100,000 for two subscriber systems).

The book "Advanced Technologies of Quantum Key Distribution" contains the results of scientific research eliminating the abovementioned disadvantages. In view of this, the book was divided into two sections—the first one "Modern QKD Technologies" is devoted to ad‐ vanced protocols and systems for key distribution using quantum technologies, and the sec‐ ond part "Quantum Channel Construction" is related to corrective measures for improving the quantum channel efficiency.

There are also other quantum technologies of information security (such as quantum secure direct communication, quantum secret sharing, quantum stream cipher, and quantum digi‐ tal signature), but in practice, these have not been extended beyond the laboratory experi‐ ments. However, practical implementation of these quantum technologies is also faced by some technological difficulties.

QKD and other quantum technologies, therefore, represent an important step toward im‐ proving the security of modern (and future) information and communication systems against cyberattacks, but many theoretical and practical problems must be solved for a wide practical use of them.

> **Professor Sergiy Gnatyuk** National Aviation University Ukraine

**Section 1**

**Modern QKD Technologies**

**Modern QKD Technologies**

The book "Advanced Technologies of Quantum Key Distribution" contains the results of scientific research eliminating the abovementioned disadvantages. In view of this, the book was divided into two sections—the first one "Modern QKD Technologies" is devoted to ad‐ vanced protocols and systems for key distribution using quantum technologies, and the sec‐ ond part "Quantum Channel Construction" is related to corrective measures for improving

There are also other quantum technologies of information security (such as quantum secure direct communication, quantum secret sharing, quantum stream cipher, and quantum digi‐ tal signature), but in practice, these have not been extended beyond the laboratory experi‐ ments. However, practical implementation of these quantum technologies is also faced by

QKD and other quantum technologies, therefore, represent an important step toward im‐ proving the security of modern (and future) information and communication systems against cyberattacks, but many theoretical and practical problems must be solved for a wide

> **Professor Sergiy Gnatyuk** National Aviation University

> > Ukraine

the quantum channel efficiency.

VIII Preface

some technological difficulties.

practical use of them.

**Chapter 1**

Provisional chapter

**Security of Quantum Key Distribution Protocols**

DOI: 10.5772/intechopen.74234

Quantum key distribution (QKD), another name for quantum cryptography, is the most advanced subfield of quantum information and communication technology (QICT). The first QKD protocol was proposed in 1984, and since then, more protocols have been proposed. It uses quantum mechanics to enable secure exchange of cryptographic keys. In order to have high confidence in the security of the QKD protocols, such protocols must be proven to be secure against any arbitrary attacks. In this chapter, we discuss and demonstrate security proofs for QKD protocols. Security analysis of QKD protocols can be categorised into two techniques, namely infinite-key and finite-key analyses. Finite-key analysis offers more realistic results than the infinite-key one, while infinite-key analysis provides more simplicity. We briefly provide the background of QKD and also define the basic notion of security in QKD protocols. The cryptographic key is shared between Alice and Bob. Since the key is random and unknown to an eavesdropper, Eve, she is unable to learn anything about the message simply by intercepting the ciphertext. This phenomenon is beyond the ability of classical information processing. We then study some tools that are used in the derivation of security proofs for the infinite- and finite-length key limits.

Keywords: quantum cryptography, QKD, protocols, security, finite-security,

Quantum cryptography, specifically QKD, has been built based on physical concepts associated with quantum mechanics. In contrast to conventional cryptography, whose security is based on the complex computational and mathematical algorithms for security, it is founded on the uncertainty relations, Bell's inequalities, entanglement or non-locality [1]. The implementation of QKD consists of detectors, repeaters, quantum memories and decoy states [2–4]. These concepts form the basis of security proofs [5]. In order for Eve to obtain the secret key,

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Security of Quantum Key Distribution Protocols

Mhlambululi Mafu and Makhamisa Senekane

Mhlambululi Mafu and Makhamisa Senekane

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74234

entanglement, QKD schemes

1. Introduction

Abstract

#### **Security of Quantum Key Distribution Protocols** Security of Quantum Key Distribution Protocols

DOI: 10.5772/intechopen.74234

Mhlambululi Mafu and Makhamisa Senekane Mhlambululi Mafu and Makhamisa Senekane

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74234

#### Abstract

Quantum key distribution (QKD), another name for quantum cryptography, is the most advanced subfield of quantum information and communication technology (QICT). The first QKD protocol was proposed in 1984, and since then, more protocols have been proposed. It uses quantum mechanics to enable secure exchange of cryptographic keys. In order to have high confidence in the security of the QKD protocols, such protocols must be proven to be secure against any arbitrary attacks. In this chapter, we discuss and demonstrate security proofs for QKD protocols. Security analysis of QKD protocols can be categorised into two techniques, namely infinite-key and finite-key analyses. Finite-key analysis offers more realistic results than the infinite-key one, while infinite-key analysis provides more simplicity. We briefly provide the background of QKD and also define the basic notion of security in QKD protocols. The cryptographic key is shared between Alice and Bob. Since the key is random and unknown to an eavesdropper, Eve, she is unable to learn anything about the message simply by intercepting the ciphertext. This phenomenon is beyond the ability of classical information processing. We then study some tools that are used in the derivation of security proofs for the infinite- and finite-length key limits.

Keywords: quantum cryptography, QKD, protocols, security, finite-security, entanglement, QKD schemes
