Quantum key distribution theory and practice

3.3 Assumption and protocol

Untill now the research considered a QKD as the only one key exchange which is secure. After their experience and verification, they came up with same characteristics to show us that this system stayed a secure system and the eternel system secure. Let us enumerate them.

1. This system give an guarantee to detect the Eve presence in the channel;

2. The key is absolutely secure that does not depend to the complexity of the algorithm or the technology used by Eavesdropper to attack.

Having those assumptions with a properties of quantum mechanics, quantum cryptography provide two kinds of protocols. All the protocols are able to detect the Eavesdropper in the channel and have the unconditional security.

3.4 Protocols Using Heisenberg's

There are many protocols using this notion of HUP but for us, we will focus on those which are more used and discovered before. We may have in mind that all the protocols follow the same structure⁶.

Prepare and send protocol

After Weisberg publish a paper where he introduced the concept of quantum mechanics in communication, Bernett and Bassard in 1984 come up with a new revolutionnary idea which was the first proposal of QKD protocol using totaly HUP (based on quantum properties) notion. This protocol is the oldest for quantum cryptography, based on basis⁷ which are quite related to the polarization notion. We have the rectilinear and the diagonal basis for BB84. Quantum protocol can be describe in two steps or phases, quantum and classical one. Let us describe firstly quantum phase and classical phase after.

Quantum phase

Any message passing through in the computer are converted into zeroes and ones which are the informatic unity in classical information theory. In BB84, there exist a correspondant unity for quantum information to express information. Using Dirac notation, we express the information unity with a braket as |øi, |1i or |xi and its call qubits ⁸. Other definition, we call a qubit a superposition of zeroes and ones (|00i, |01i, |10i) , is described by complex number with an argument 1 belong the set

{á|0i + /3|1i : |á|² + |/3|² = 1;á,/3 ? C}, (3.4.1)

we take |0i and |1i as two references qubits, corresponding to two orthogonal states in a quantum system.

⁶Structure means the fonctionnality is the same but few differents we can find but in general is the same

⁷BB84 is the main protocol and the remaind follow the way that its works the difference is few certain have a difference just in basis used to send the information

⁸Quantum bits

Section 3.4. Protocols Using Heisenberg's Page 17

Figure 3.3: Transmission photon by Alice to Bob

Figure 3.4: Detection of photon by Bob using states measurement

1. In BB84, Alice sends a sequence of photon to Bob, each independantly choose one of the four polarization (the four polarization are vertical, horizontal, 45% and 135% you can have an idea checking the figure down).

2. For each polarization, Bob will choose one base for measurement to achieve the result

3. Bob will records the result and his measurement bases and after, he will publicly acknowledges his receipt other signal.

Classical phase

In this phase the entities have a following steps

1. Alice broadcasts her bases of measurement, Bob broadcasts his bases of measurements

2. Alice and Bob discard all events where they use different bases for a signal

3. To test for tempering, Alice randomly choose a fraction, if all remaining events as test events, she publicly broadcasts their position and polarization

4. Bob broadcasts the polarizations of the test events

Section 3.5. Entaglement base to protocol Page 18

Figure 3.5: Data transmit between two parties using basis

5. Alice and Bob compute the error rate of the test events. If the compution of error rate is large than some prescribed threshold value, say 11% they about otherwise, they proceed to the next step (This step is where Alice and Bob detect Eve presence)

6. Alice and Bob each convert the polarization data of all remaining data into a binary string called a raw key. They can perform classical post-procesing such as error correction and privacy amplification to generate a final key.

With quantum mechanics properties, the security is a efficiency and the Eavesdropper can use any method of attack Alice and Bob will detect her. The work of [Zha09] explain other notion for the efficiency security.

3.4.1 B92 protocol . This protocol is a derivative of BB84 protocol. It was proposed by Charles Bernett in 1992. B92 have the same function then BB84 but the difference is just the half part of fonctionality from BB84. The encoding of one state for example |ø) composed by {|0), |1)} we can encode each element of the set in this way the first element in the set will be encode with rectilinear basis which is correspond to 0^o and |1) encode in diagonal basis this according to [Hai14]. There exist also other variants QKD protocols using the notion of Heisenber Uncertainty Principale as you can see in many book where they are talking about QKD like [Hai14]. We can enumerate other protocols using Heisenberg like, Six-State Protoco(SSP) proposed by Posquinucci, Gusin in 1999 the different with BB84 instand of two state and here the use one.