Quantum key distribution theory and practice

Quantum Key Distribution : Theory and Practice

Grace Mupoyi Ntuala ( [e-mail])
African Institute for Mathematical Sciences (AIMS)

Senegal

Supervised by: Dr. Kassem Kalach
[e-mail]

Institute for Quantum Computing

13 June 2015

Submitted in Partial Fulfillment of a Masters II at AIMS

Abstract

Information security has increasingly been important for individuals and organizations. For example, secure communications in financial, commercial and military applications are vital. Cryptography is the science of all aspects of information security. In particular, public-key cryptography is necessary to provide secure communications over the Internet.

Unfortunately, based on the assumed difficulty of some mathematical problems, public-key cryptography (includes ECDSA, ElGamal, and RSA schemes), would be broken with either advances in algorithms or the advent of quantum computers. On the other hand, quantum cryptography, based on the laws of quantum physics, provides perfect security even against the most general quantum attacks.

Quantum key distribution (QKD), a branch of quantum cryptography, allows two legitimate parties to expand a previously shared secret over a public quantum channel. Importantly, eavesdropping can now be detected, this is impossible in classical cryptography. Although many QKD protocols have been proposed, they all face technological challenges in practice, thus making them not suitable in many applications. In this project, we survey the most promising protocols, and compare them from theoretical and practical point of view. In particular, we study how and where they can be practical, and try to propose new applications.

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Declaration

I, the undersigned, hereby declare that the work contained in this essay is my original work, and that any work done by others or by myself previously has been acknowledged and referenced accordingly

Grace Mupoyi Ntuala,

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Contents

Abstract i

EPIGRAPHY 1

INTRODUCTION 1

1 Classical Cryptography 2

1.1 Definition 2

1.2 Security concepts 3

1.3 Cryptosystem 3

1.4 Diffie-Hellman Key Exchange 6

1.5 Information Theory 7

2 Fundamentals of Quantum Mechanics 8

2.1 Polarization 8

2.2 Circular polarization 9

2.3 Heisenberg Uncertainty principle 10

2.4 Entanglement 11

2.5 No-cloning Theorem 12

3 QKD protocols 14

3.1 QKD with classical notion 14

3.2 Main operation of key exchange technic of QKD 14

3.3 Assumption and protocol 16

3.4 Protocols Using Heisenberg's 16

3.5 Entaglement base to protocol 18

3.6 Attacks on a QKD channel 19

4 QKD implementation technologies 21

4.1 Sources for QKD 21

4.2 Detectors 23

5 QKD Application 25

5.1 Network 25

5.2 Databases future work 30

CONCLUSION 1

References 4

EPIGRAPHY

1

The best thing is in the thorns

by Jean Kanyinda Bidiku

1

INTRODUCTION

Naturally, human had a desire to communicate secretly since the beginning of civilization. Many ancient societies Egypt, India, china, Japan, developped methods of secret communication like globaly a new science where the goal was to keep with innovations and evolution that science progressed and Stephen Weisner proposed a new concept of crypthograhy in conjonction with a quantum mechanics, a subfield of quantum physics, and it was publish in a seminal paper titled Conjugate coding. But in 1983, with SIGACT News, Stephen Weisner proposition was eventually published in that document, he showed how two messages can be stored or transmited by encoding in two conjugate observable, Using physical notion, such as linear or circular polarization so that either of which may be recieveed and decoded. The physical notion cannot use both in the same time.

After SIGACT News published Weisner proposition of quantum conjugate coding, the field red team of quantum cryptography red was created. Using Weisner work, there are same peoples based on it 1984, charles H. Bernnett of the IBM, Thomas J. Watson research center and Gilles Brassard come up with a concept of secure communication based on conjugate observable. After six years, an other person proposed a different approach to quantum key distribution which is based on pecullar quantum correlations known as quantum entanglement. We may know that after people developped classical crytography one of the most promising. They wanted to find other way to keep secret message which will be more secure since RSA crypto-system have a high level of security with a discrete logarithm, factoring, or Diffie-Hellmann problem, quantum cryptography come with a QKD to solve this problem and that provide a small size of key between sender and receiver.

The combination of cryptography and quantum mechanics notions give this new field a condition to be a power field in terms of security. As this field used a photon as matter for transmission message and the two notions of quantum mechanics use in this field have an ability to detect any kinds of attack in the channel. In general, quantum cryptography have a goal which is to perform tasks that are impossible with conventional cryptography. Quantum cryptography has an avantage since the security is based on physical laws such no-cloning theorem, heisenberg principle. Having those notion which QKD as tool of quantum cryptography, quantum bit and quantum coin tossing, quantum cryptography was prove that this cryptography is unconditionally secure.

In our thesis we will talk about Quantum Key Distribution and we will develop five chapters. In the first chapter we will discuss about classical cryptography, in second chapter, we will focus on fundamental of quantum mechanics, in the third we will try to speak about QKD protocols. Chapter four we will focussed on the different implementations of QKD and in the last chapter we will talk about QKD applications. At the end of this thesis, we will propose, as a contribution in this new field of security, a new application of QKD in Business Intelligence. We hope there will be an outcome for a new generation of Business Intelligence.

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1. Classical Cryptography

In this section, we will talk around all notions in cryptography. Since longtime, in the world to keep secret message was very important. That trick in mind has been with us since we moved out of caves, started living in groups and decided to take this civilization idea seriously. As soon as there were different groups or tribes, the idea that we had to work against each other surfaced and proliferated, along with rank violence, secrecy, and crowd manipulation. The earliest forms of cryptography were found in the cradle of civilization, which comes as no surprise, the regions currently encompassed by Egypt, Greece and Rome. In Rome when Julius Cesar Emperor, wanted to send a message through the war to inform his army generals about something, he was writing a message covertly by shifting the alphabet letters so that if another person foundn'ta message can not understand what is going on just the intendedreceiver would knows how to read the message.