Quantum Key Distribution Protocols
During the time when THANOS was expanding it’s control over the universe, as they were having much power they had to also take care of their enemies(The Avengers) and be updated about their enemies plans. Avengers knew they were being watched but they had to execute plans to stop THANOS from gaining anymore cities and also defeat them. So they had to maintain in direct touch with different fighters or universes like ASGARD ,Captain Marvel, Guardians of Galaxy at the same time. Ebony Maw (I have attached a picture, don't worry)being a very intelligent teammate of Thanos was given a task to decode all the conversation between the Avengers and their allies to THANOS.
Avengers earlier used the classical way to share the info among their team members of RSA encryption method .But Ebony Maw kidnapped a great Scientist Dr. Peter Shor and with his help he could break the RSA encrypted messages which was a big problem and setback for the avengers, due to which all their conversation were interrupted .Now they didn’t have any safe way to carry out their conversation.
On seeing the current situation of the Avengers and for the only hope of mankind to survive Nick Fury brought 2 of the Greatest Scientists of All time(G.O.A.T) to the Avengers headquarters Dr. Charles Bennett and Dr. Gilles Brassard.
They worked day and night and came up with a protocol called BB84(I know Shor’s algo was made in 1994 and BB84 was in 1984,but this was the only way to make a story).BB84 was like a bomb for everyone and even Ebony Maw couldn’t find the encryped messages now,which gave an edge to the AVENGERS .Avengers didn’t stop there and took help some more protocols to maintain their conversation and save the people of Earth.After 20 years,when Banner was hanging out with Tony’s daughter who was also a Techie(like father like daughter) ,she asked to explain about the protocols to which Bruce Banner (HULK) started telling her about the basics of the cryptography and the protocols(BB84,E91,B92) they had used to win the war.
1. Introduction
Classical cryptography can be divided into two major branches; secret or symmetric key cryptography and public key cryptography, which is also known as asymmetric cryptography. Secret key cryptography represents the most traditional form of cryptography in which two parties both encrypt and decrypt their messages using the same shared secret key. While some secret key schemes, such as one-time pads, are perfectly secure against an attacker with arbitrary computational power , they have the major practical disadvantage that before two parties can communicate securely they must somehow establish a secret key. In order to establish a secret key over an insecure channel, key distribution schemes basd on public key cryptography, such as Diffie-Hellman, are typically employed.
In contrast to secret key cryptography, a shared secret key does not need to be established prior to communication in public key cryptography. Instead each party has a private key, which remains secret, and a public key, which they may distribute freely. If one party, say Alice, wants to send a message to another party, Bob, she would encrypt her message with Bob’s public key after which only Bob could decrypt the message using his private key. While there is no need for key exchange, the security of public key cryptography algorithms are currently all based on the unproven assumption of the difficulty of certain problems such as integer factorization or the discrete logarithm problem. This means that public key cryptography algorithms are potentially vulnerable to improvements in computational power or the discovery of efficient algorithms to solve their underlying problems. Indeed algorithms have already been proposed to perform both integer factorization and solve the discrete logarithm problem in polynomial time on a quantum computer.
While the advent of a feasible quantum computer would make current public key cryptosystems obsolete and threaten key distribution protocols such as Diffie-Hellman, some of the same principles that empower quantum computers also offer an unconditionally secure solution to the key distribution problem. Moreover, quantum mechanics also provides the ability to detect the presence of an eavesdropper who is attempting to learn the key, which is a new feature in the field of cryptography. Because the research community has been focused primarily on using quantum mechanics to enable secure key distribution, quantum cryptography and quantum key distribution (QKD) are generally synonymous in the literature.
The focus of this article is to survey the most prominent quantum key distribution protocols and their security from the perspective a computer scientist and not that of a quantum physicist. In order to understand these protocols, however, we briefly describe the necessary principles from quantum mechanics.
Fundamentals of Quantum Cryptography
The basic model for QKD protocols involves two parties, referred to as Alice(Avengers) and Bob(other Allies), wishing to exchange a key both with access to a classical public communication channel and a quantum communication channel. This is shown in the given figure. An eavesdropper, called Eve(Ebony Maw), is assumed to have access to both channels and no assumptions are made about the resources at her disposal. With this basic model established, we describe in layman’s terms the necessary quantum principles needed to understand the QKD protocols.
BB84 protocol, proposed in 1984 by Bennett and Brassard — that’s where the name comes from. The idea is to encode every bit of the secret key into the polarization state of a single photon. Because the polarization state of a single photon cannot be measured without destroying this photon, this information will be ‘fragile’ and not available to the eavesdropper. Any eavesdropper (called Eve) will have to detect the photon, and then she will either reveal herself or will have to re-send this photon. But then she will inevitably send a photon with a wrong polarization state. This will lead to errors, and again the eavesdropper will reveal herself.
The protocol then runs as follows. Alice sends a sequence of pulses (for instance, femtosecond pulses with 80 MHz rep. rate), each of which, ideally, contains a single photon polarized differently. Alice encodes zeroes into H-polarized(Horizontally) photons while unities she encodes into V-polarized photons(vertically) (red arrows in Fig. 1). But this happens only in half of the cases. The other half of bits, chosen randomly, are encoded using a diagonal polarizationbasis (blue arrows in Fig. 1). Then, the ‘D’ polarization corresponds to zero and the ‘A’ polarization, to unity.
The receiver, Bob, measures the polarization using a standard setup (a PBS or a Glan prism with two single-photon detectors in the output ports, or a calcite crystal also followed by two detectors). This way Bob can distinguish between H and V polarizations if he uses the HV basis (further denoted as ‘+’). But in half of the cases Bob randomly changes his basis (the orientation of his prism) to AD (denoted as ‘X’).After a certain number of bits has been transmitted (and all photons have been detected and destroyed!), Bob publicly announces which basis he used for each bit. Alice then says in which cases they used the same bases. They throw out the bits where they used different bases, and leave only those where they used the same one. After this procedure (key sifting) the length of the key is reduced twice, but what remains is random and coincides for Alice and Bob. Then, they check if there was eavesdropping. To this end, they take a part of the key for instance, (10%) and compare it. This procedure is also public, but these 10% are then discarded. If the Fig.1 eavesdropping took place, the key would contain errors. Then the whole key is thrown out and the procedure is repeated again. The table below gives an example of transmitting 8 bits of a secret key. After the key sifting, only 4 bits are left.
Alternative Sources to read: https://www.youtube.com/watch?v=u_K9jPBrOwA
This was Avengers first step in winning but they had to keep improving as Ebony Maw was very clever person .
B-92 PROTOCOL
In 1992, Charles Bennett proposed the B92 protocol in his paper “Quantum cryptography using any two non-orthogonal states”. B92 protocol is a modified version of the BB84 protocol with the key difference between the two being that while BB84 protocol uses four different polarization states of photon, the B92 protocol uses two (one from the rectilinear basis, conventionally H-polarization state and one from the diagonal basis, conventionally +45° — polarization state). The B92 protocol can be summarized in the following steps-
· Alice sends a string of photons in either H-polarization state or +45° — polarization state, chosen randomly. H-state will correspond to the bit ‘0’ whereas +45°-state will correspond to the bit ‘1’.
· Bob randomly choses between rectilinear and diagonal basis, to measure the polarization of the received photon.
· If Bob is measuring in the rectilinear basis, there are two possible circumstances: if the incident photon is H-polarized, then the measurement outcome will be H-state with probability 1 whereas if the incident photon is +45°-polarized, then the measurement outcome will be either H-state or V-state with probability 0.5. Thus, if only the outcome is V-state, Bob can infer confidently that the incident polarization state of the photon is ‘+45°’.
· Similar argument will be applicable if Bob is measuring in the diagonal basis, where the measurement outcome of -45°-state will indicate that the incident polarization state of the photon is ‘H’.
· After the transmission of the string of photons, Bob announces the instances in which the measurement outcome was either ‘V’ or ‘-45°’ and the rest are discarded by both of them. These results can be used to generate a random bit string between Alice and Bob.
For the verification of eavesdropping, Bob and Alice publicly share a part of the generated random bit string and if the error crosses a tolerable limit, the protocol is aborted. If not, they now have been able to generate a secure and symmetric key between them.
After telling about this protocol Banner saw that her interest in Quantum Cryptography was very much increasing and took no time to tell her the other greates protocol as she was becoming very much impatient about how the protectors changed the phase of the war against THANOS. She was like
Alternative Sources to read:
E-91 Protocol
The important principle on which QKD is based is the principle of quantum entanglement. It is possible for two particles to become entangled such that when a particular property is measured in one particle, the opposite state will be observed on the entangled particle instantaneously. This is true regardless of the distance between the entangled particles. It is impossible, however, to predict prior to measurement what state will be observed thus it is not possible to communicate via entangled particles without discussing the observations over a classical channel. The process of communicating using entangled states, aided by a classical information channel, is known as quantum teleportation and is the basis of Eckert’s protocol.
Let us give a brief introduction of the quantum E91 protocol. There are two groups of measurement basis: Z−basis:Bz={|0⟩,|1⟩} and X−basis:Bx={|+⟩,|−⟩}. Alice and Bob randomly choose Bz or Bx to measure the received particle each time. The E91 protocol can be described in the following steps:
· The source center chooses the EPR pair(Bell State) |ϕ+⟩=1/√2(|00⟩+|11⟩), sends the first particle |ϕ+⟩1 to Alice and second particle |ϕ+⟩2 to Bob.
· Alice and Bob randomly choose Bz or Bx to measure their received particle. They record the measurement result and broadcast the measurement basis which they used through the classical channel.
· Alice and Bob know the choice of both parties. They divide the measurement result into two groups: one is the decoy qubits Gd where they choose different measurement basis and another is the raw key qubits Gk where they choose the same measurement basis.
· The group Gd is used to detect whether there is a eavesdropping. Gd is always entangled without eavesdropper in an ideal environment. If there is bit error in Gd, which means that there is also a eavesdropper, Alice and Bob think that the quantum channel is not safe and they will interrupt this communication and restart a new one.
· If the quantum channel is safe, Gk can be used as the raw keys because Alice and Bob can receive the same measurements. Both Alice and Bob agree on that the measurement |0⟩ represents the classical bit 0, while the measurement |1⟩ represents the classical bit 1.
· The E91 protocol ends successfully.
On getting all the knowledge of the protocols, Tony’s daughter was very much surprised about how much struggle the people had to do to gain the freedom they had today and was very much interested in Quantum Cryptography, and wanted to carry out the legacy of being the changemakers like her father Tony and her grandpa Howard Stark she decided to take Quantum Cryptography as her majors to save earth from any further dangers and maintain the communication among certain galaxies and that day the next savior of EARTH was born.
Alternative Sources to read:
https://journals.sagepub.com/doi/full/10.1177/1550147718778192,
https://www.mpl.mpg.de/fileadmin/user_upload/Chekhova_Research_Group/Lecture_4_12.pdf
https://github.com/amityadav10101010101010101010/Quantum-Communication-Protocols
QKD Code Implemented using QuNetSim:
What Next?
E-91 Protocol used Entangled states….but what if we do entanglement between two entangled states….Yes…That’s a Hyperentangled state.
Use this circuit to send one state to Alice and the other one to Bob and this will make it very very difficult for getting the initial state by the Eavesdropper.
(PDF) Experimental realization of quantum teleportation of an arbitrary two-qubit state using a four-qubit cluster state (researchgate.net)
But as the no. of Qubits increase here…the chance of error also increases which will lead in decreasing the efficiency of the information to be transferred over the channel. So we need to find a way to increase our efficiency to transfer the information so the error is decreased and the information to be efficiently transmitted.
