Why Quantum Cryptography Will Be The Future of Secure Communications?
Firstly for those who are hearing the term of “Cryptography” for first time, Cryptography is a method of storing and transmitting data in a particular form so that only those for whom it is intended can read and process it. It is most often associated with scrambling plain-text (ordinary text, sometimes referred to as clear-text) into cipher-text (a process called encryption), then back again (known as decryption).
Objectives of Cryptography
1) Confidentiality (the information should not be understood by anyone other than whom it was intended)
2) Integrity (the information cannot be altered in storage or transit between sender and intended receiver without the alteration being detected)
3) Non-repudiation (the creator/sender of the information cannot deny at a later stage his or her intentions in the creation or transmission of the information)
4) Authentication (the sender and receiver can confirm each other’s identity and the origin/destination of the information)
Usage of Cryptography
As the latest saying goes “Data is the new Oil”. So where there is Data, there needs to be Security for it. Data is part of all the fields ranging from Manufacturing industries, Banking, Telecom, Automotive etc. As a result Cryptography and Security to data has become the important part of all the fields.
Let me slightly give this a touch of me!! 😜
In Automotive,
Data is generally the information generated from various ECU’s and Sensors which needs to be stored safely and even transmitted securely between the Data Center or the Other Cars / Infrastructure thus creating a Connected Car environment.
Classical Cryptography
This is the most ancient cryptographic form. There are two basic components of Classical Cryptography: Substitution and Transposition
In Substitution ciphers, letters are replaced by other letters.
In Transposition ciphers, the letters are arranged in a different order.
Moreover these ciphers may be further categorised into two mechanisms:
Mono-alphabetic : Only one substitution/ transposition is used.
Poly-alphabetic : Not just one but several substitutions/ transpositions are used thus increasing the security.
Several such ciphers may be concatenated together to form a product cipher and this was the basis of Modern Cryptography too.
Modern Cryptography
Modern Cryptography relies on publicly known mathematical algorithms for coding the information. Secrecy is obtained through a secret key which is used as the seed for the algorithms. The computational difficulty of algorithms, absence of secret key, etc., make it impossible for an attacker to obtain the original information even if he knows the algorithm used for coding. It requires parties interested in secure communication to possess the secret key only.
There are mainly two modern cryptography techniques:
Symmetric Encryption also called Private-key Cryptography
Asymmetric Encryption also called Public-key Cryptography
These cryptography mechanisms are categorized on the basis of number of keys involved in the whole process (Encryption and Decryption).
Symmetric Encryption (Private-key Cryptography)
Symmetric Encryption is a technique which allows the use of only one key for performing both the encryption and the decryption of the message. Based on the key used for encryption, as this type of encryption technique uses private-key / secure-key for encryption, it is called Private-key cryptography.
Symmetric encryption algorithms executes faster and are comparatively less complex; As a result they are used for transmission of bulk data.
Most commonly used Symmetric encryption algorithms are DES, 3 DES, AES, RC4.
Block Ciphers
The Symmetric encryption technique in which plain binary text is processed in blocks (groups) of bits at a time; i.e. a block of plain-text bits is selected and a series of operations is performed on this block to generate a block of cipher-text bits. The number of bits in a block is fixed. For example, the schemes DES and AES have block sizes of 64 and 128 respectively.
Stream Ciphers
The Symmetric encryption technique in which plain binary text is processed one bit at a time i.e. one bit of plain-text is taken, and a series of operations is performed on it to generate one bit of cipher-text. Technically, stream ciphers are block ciphers with a block size of one bit.
Examples of Symmetric Encryption
Asymmetric Encryption (Public-key Cryptography)
Asymmetric Encryption technique uses a pair of keys (private key and public key) for encryption and decryption respectively.
It uses the public key for the encryption of the message and the private key for the decryption of the message. Based on the key used for encryption, as this type of encryption technique uses public-key for encryption, it is called Public-key cryptography.
The most common asymmetric encryption algorithms are Diffie-Hellman and RSA algorithm.
Comparative Analysis of Symmetric and Asymmetric Encryption
Breaking Symmetric Encryption
In symmetric encryption technique, Encryption algorithm and related key are kept secret. Breaking the system is hard due to large number of possible keys.
Consider an example for key of 128 bits long, there are:
2¹²⁸ — Possible keys to check
which is equivalent to 10³⁸ using brute force.
Brute forcing 10³⁸ possible keys is not impossible but it is difficult and time consuming with respect to the present available computing power.
Moreover, the fundamental difficulty in Symmetric encryption is not decoding the encryption algorithm or the related key. It is actually the key distribution to parties who wants to exchange messages. Care should be taken such that the key which is same for encryption and decryption in this technique is not eavesdropped.
Breaking Asymmetric Encryption
The Public-key encryption algorithms use some mathematical algorithms which have the property that some computations are easy in one direction (as for example computing the product of two special numbers) but very difficult in the opposite direction (in the example just mentioned, given the product of the two numbers find the two original special numbers).
The most widely used Asymmetric encryption is the RSA algorithm, which is based on factoring out product of two large primes.
The best known algorithm requires the solution time proportional to:
Now here comes the “Quantum Computing”
Quantum Computing algorithm for Factoring out product of two prime numbers:
In 1994, Peter Shor from the AT&T Bell Laboratory showed that in principle a Quantum Computer could factor a very long product of primes in seconds.
Shor’s algorithm time computational complexity is
What is Quantum Computing ?
Quantum Computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.
Quantum computer is different from binary digital electronic computers which are based on transistors. The common digital computing requires that the data be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits or qubits, which can be in superpositions of states.
With the quantum computers, we can store large amount of data which requires 2^n bits in normal computer within n qubits only. Thus decreasing the data size and increasing the computing power. The computing power in Quantum computers is hard to believe and far higher than the normal present day computers and super-computers.
Quantum Computers are based on the physical principles of nature than the mathematical formulations.
Let’s get into some physics…
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” — Albert Einstein
Entanglement is known to be the exchange of quantum information between two particles at a distance. It is also called the correlation between the qubits. Derived from Schrodinger wave equation.
The property of knowing the possible state of the next qubits based on the state of current qubit is called entanglement.
Superposition is known to be the uncertainty of a particle (or particles) being in several states at once (which could also involve the exchange of quantum information for a particle that is known to be in several locations simultaneously). Derived from Heisenberg Uncertainty Principle.
The famous physicist R. Feynmann suggested that a qubit occupies all the states between 0 and 1 simultaneously, but collapses into 0 or 1 when observed physically. A qubit can therefore encode an infinite amount of information, but most of this information is useless as it can never be observed.
The property of being able to exist in multiple states is called superposition.
Still Confused ? If Yes, Check this article!! 😃
“If you aren’t confused by quantum mechanics, you haven’t really understood it.” — Niels Bohr
Elements of Quantum Theory
Light waves are propagated as discrete quanta called photons.
They are mass-less and have energy, momentum and angular momentum called spin. Spin carries the polarization.
If we put a polarization filter on its way, a photon may pass through it or may not.
We can use a detector to check of a photon has passed through a filter.
“The more success the quantum theory has, the sillier it looks” — Albert Einstein
Polarization of Photons
A photon has the capability to spin in all three states i.e either vertical or horizontal or diagonal at the same instance of time which is nothing but the concept of Superposition as defined above.
Polarization is a concept of passing photon through a filter so that it has occupies a particular spin which is mostly either vertical or horizontal or diagonal. Polarization of a photon is performed using polarization filters.
Types of Polarization
There are 2 types of polarization's:
1. Rectilinear Polarization (+)
2. Diagonal Polarization (X)
When a photon is polarized using say X filter (Diagonal Polarization), then to get the original spin of the photon only X filter should be used.
If + filter (Rectilinear Polarization) is used on the photon which is polarized using X filter, then the original polarization will be absorbed by the polarized photon and the polarization will be now in different spin than the original spin of photon.
Rectilinear Polarization (+) => Horizontal Spin (–), Vertical Spin (|)
Diagonal Polarization (X) => Left Diagonal Spin (\), Right Diagonal Spin (/)
For example, a horizontal spinning photon when passed through a wrong filter (i.e diagonal filter) will lead to diagonal spin, which is incorrect.
Decoding Quantum to Binary
Now based on the spins obtained from the quantum particles like photon, the spin state can be converted to the binary value using the below table.
Quantum Key Distribution (QKD)
Quantum Key Distribution also called QKD is not something different, it is actually the Quantum Cryptography. The Quantum Cryptography actually deals only with the random key generation using principles of nature i.e. quantum mechanics, nothing more than this. So you can assume Quantum Cryptography is nothing but Quantum Key Distribution (QKD).
Have you got a question “Why Quantum Cryptography just deals with Random Number Generation ?”
The secret key in the Modern cryptographic algorithms is a random number of some appropriate length. So to generate a key using modern cryptographic algorithms on a computer we need a good RANDOM NUMBER GENERATOR i.e. a program which generates a sequence of numbers which are enough random to be acceptable as secret keys for the chosen cryptographic algorithm. The present day random number generation algorithms are impossible to generate pure random numbers since we have to use mathematical formulas and functions which are deterministic.
Now if have a few set of random numbers generated using a specific Random Number Generation algorithm, then it is easy for the Quantum Computer to analyse these sample of random numbers and find the random number generation algorithm. This is nothing but hacking or else breaking the cryptographic algorithm. When you know the pattern of the most confidential part of the cryptographic algorithm i.e secret key, I think there is nothing more called secure and confidential. So when the Quantum Computers come into actual use in the future, the present random number generators for cryptographic algorithms are no more than just a deterministic number generators and are not any more RANDOM.
Moreover it is called Quantum Key Distribution because we previously had a problem with key distribution in the Modern Cryptographic algorithms. There was a possibility of secret-key being eavesdropped. With the possibilities of principles of quantum mechanics we can now easily detect the eavesdropping and if secret-key is found to be eavesdropped, we can simply abandon the secret-key being used for communication and generate a new secret key thus enhancing the security and confidentiality with easing the key distribution process.
Process of Quantum Key Distribution
Entangled Photos are connected photons, the actions performed on one affect the other, even when separated by great distances. The spins states of these photons are generated by particular angle of the solid crystal. Such entangled photons are used to generate the Quantum Key.
Now consider the classical and fictional cryptographic example of the most famous couple in the world of cryptography. Some message transmission between ALICE and BOB. Let us consider Alice as the sender, Bob as the receiver and Eve as the eavesdropper who is also most famous person and the reason for us to learn this thing of cryptography 😂.
Unlike Modern Cryptography which uses only single channel for key transmission as well as data transmission, Quantum Cryptography involves two communication channels: Classical Channel and Quantum Channel.
Classical Channel
A communication channel in which information is transmitted in the form of bits i.e. information is exchanged in the binary form (Digital signals having 0 or 1 state). This channel is used to verify that no eavesdropping has taken place and for encrypted data transmission after Quantum based secret-key generation.
Quantum Channel
A communication channel in which information is transmitted in the form of quantum bits or qubits i.e. information is exchanged in the quantum form (Photons having some polarized spin states). This channel is used only for Random Secret Key Generation.
As we have various algorithms like RSA, AES, DES etc. in Modern Cryptography, even Quantum Key Distribution aka. Quantum Cryptography too has different type of protocols / algorithms. Some of the popular and widely researched such protocols are: BB84, T12 protocol, Decoy state protocol, SARG04, Six-State protocol, E91 protocol, BBM92 protocol and there are many other too. Get the list here!!
Moreover these protocols can be again categorized mainly into two based on the principle they use to provide the Quantum Key Distribution. They are :
1) Protocols Utilizing Heisenberg’s Uncertainty Principle
The Heisenberg Uncertainty Principle states that the product of uncertainties in related physical quantities (e.g. position and momentum, energy and time, etc.) has a finite lower bound. This arises from the fact that the momentum and position operators do not commute. Source: WikiBooks
Don’t worry if the above explanation of HU Principle made you dumb then here is the simple version of it, suppose if we know ‘x’ really, really well. Then we cannot know ‘p’ very very well at all i.e. if you know the position of a particle and you measure the momentum, it disturbs the position — thus you are less certain of its position.
In those protocols utilizing Heisenberg’s Uncertainty Principle like BB84 Protocol which is the most famous Quantum Key Distribution technique and also the first QKD protocol, Alice transmits a random secret key to Bob in the form of a stream of photons in which the secret key’s bits are encoded as the polarization of the photons. The basic idea of using the Heisenberg’s Uncertainty Principle is to guarantee that an Eavesdropper cannot measure the photons being transmitted to Bob without disturbing the photon’s spin state. If change in spin state is detected in the majority of photons then it is observed that the key is being eavesdropped by Eve and thus the secret-key is discarded and a new transmission is initiated in a different Quantum Channel.
Heisenberg’s Uncertainty Principle can be used to guarantee that an Eavesdropper cannot measure the photons and transmit them on to Bob without disturbing the photon’s state in a detectable way thus revealing her presence. It’s like if Eve disturbs the photon, then he can’t transmit it further and if he transmits the photon then he cannot disturb i.e. known the state of it photon.
BB84 Protocol (The First Quantum Key Distribution Protocol)
Firstly Alice randomly chooses polarization of each photon and sends the corresponding polarization state to Bob through Quantum Channel.
Now it’s the receiver Bob who chooses one of the two polarization filters. He may either use the same polarization filter as Alice has used so that he could get a perfectly correlated result or the exact opposite if he uses the different polarization filter other than which Alice has used thus obtaining an uncorrelated result. There may be cases in which the Bob does not either any result or gets an improper result because of errors in the detection or in the transmission which may due to noise in the transmission channel.
After all the quantum transmissions by Alice, Bob obtains a string of all received bits which is called the “raw key”.
Bob announces to Alice the raw key he has interpreted (i.e which bases whether diagonal or rectilinear was used and which photons were registered) through a public channel also called the classical channel. It is to be noted that he does not reveal which result he obtained.
Now Alice compares the Bob’s interpretation with the actual basis he has sent and sends back Bob only bits corresponding to the same basis. Because both have randomly chosen the basis, there may be both correlated and uncorrelated results with equal probability. Therefore, about almost 50 % of the raw key is discarded. This shorter key is called sifted key.
Now the error rate is calculated choosing at random some of the remaining bits in the sifted key which they discard later. There are two main reasons why the error rate can differ from the expected value: technical imperfections in the set-up due to presence of noise which alters the quantum data being transmitted and a potential presence of an eavesdropper who has altered the polarization states.
Now if the error rate is less than or equal to the expected, then the secret key is generated by removing the bits used for error rate calculation and thus obtained is considered as the random key for use in encrypting the data being transmitted in classical channel. Otherwise the random secret key generated is discarded if error rate is higher than the expected and a new transmission process for new key is initiated in a new quantum channel.
Check this out practically by simulating BB84 Protocol Online: Click Here
So, What if photons are cloned ?
You got a good question but the answer is very simple, you can’t never clone a photon / quantum particle. This is explained by No-Cloning Theorem.
No-Cloning Theorem
This theorem states that if you have a perfect cloning machine and when you send a rectilinear polarized photon to clone it, consider the spin state of it to be horizontal (→) or (←) which is part of rectilinear polarization then the cloning machine tries to clone the state of photon and may give the output as rectilinear polarized photon itself but the spin state of the output photon may be changed to vertical (↑) or (↓) instead of horizontal which changes its binary interpretation from 0 (Horizontal Spin State) to 1 (Vertical Spin State) as specified above in the table related to conversion of Quantum to Binary.
The same is the case when diagonally polarized photon is been tried to clone. As a result even when the photon is tried to be cloned, it is easy identify that an eavesdropper Eve is present. This problem occurs due to the definition of cloning which requests that “two of the same” are equal to the square of the original state. This leads to a contradiction of the linearity of quantum mechanics.
2) Protocols Utilizing Quantum Entanglement
Quantum entanglement is a physical phenomenon which occurs when pairs or groups of particles are generated in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance — instead, a quantum state must be described for the system as a whole. Source: Wikipedia
As per the definition we defined very simple earlier, Entanglement is the correlation between the qubits.
In those type of Protocols Utilizing Quantum Entanglement like Ekert’s Protocol also called E91 Protocol, the property of Entanglement acts as the basis of QKD. These protocols have a quantum channel in which a single photon source emits pairs of entangled photons and this acts as the Random Number Generator.
E91 Protocol (Ekert’s Protocol)
In this protocol, there exists a single photon source emits pairs of entangled polarized particles. These particles are transmitted between Alice and Bob using a quantum channel where each receive one particle from each pair.
Alice and Bob would each choose a random polarization filters to measure the received entangled polarized particles.
Now after there interpretation, similar to BB84 they would discuss using the public channel on which bases they used for their measurements. For the measurement where Alice and Bob used the same bases of polarization filter, they should expect opposite results due to the principle of quantum entanglement as described earlier. This means that if Alice and Bob both interpret their measurements as bits, they end up having a bit string which is the binary complement of each other. As a result to discuss in the public channel Bob would invert his key and they would thus share a secret key.
The presence of an eavesdropper can be detected by examining the photons whether the inequality does hold thus indicating that the photons were not truly entangled and thus there may be an eavesdropper present. Moreover in this kind of protocol where there exists a single source which emits a pair of entangled photons, it is hard even for the eavesdropper to interpret the possible polarization which Bob and Alice may interpret correctly.
In this protocol, you cannot interpret anything just with one photon which is part of an entangled pair. You need both the photons (i.e. entangled pair) to interpret anything from it.
Complications in Quantum Key Distribution
Presence of Noise in Quantum channels alters the polarization and also some time generates unpredictable polarization thus increasing the error rates.
Eavesdropper may split the photons being transmitted in the quantum channel thus taking the copy of photon without altering its polarization state as it it currently impossible to detect whether the photon received by the Bob is single photon or a split photon.
Eavesdropper may also send some extra dummy photons along with the photons sent by Alice in the quantum channel. This makes Bob hard to detect the actual photons sent by Alice and also causes Bob to detect and interpret more data from dummy photons thus spamming the Bob’s interpretations. It is similar like DDoS attacks.
Currently quantum cryptography i.e Quantum Key Distribution is still limited in distance upto 150Kms and also provides low transmission rates which makes it slightly impractical and also costly. Moreover the use of quantum channel, photon emitters and polarization detectors requires much of hardware which is too costly and also needs a proper environment to setup the whole hardware which is impractical in all the scenarios.
But rapid research in the quantum computing and quantum cryptography confirms the idea that quantum cryptography will find commercial application mostly in the field of military, space etc in the near future.
Keeping these complications apart, China and Austria jointly have sent a Quantum enabled satellite which is nicknamed as “Micius” to experiment secure communications using this concept of Quantum Key Distribution (QKD). Doesn’t it look cool!! 😎 This is how the communications in future might be…
Finally, Thanks to Cat which made you read this !!
Are you thinking deeply how this cat is related to reading this ?
Cool!! It’s the Schrödinger’s cat experiment which led to the illustration of Quantum Superposition and thus led to explore the possibilities of Quantum Particles in Computing as well as many applications of quantum mechanics.
In this exercise, an imaginary cat is hidden in a box with a flask of poison, a tiny amount radioactive material, and a Geiger counter wired to a hammer. If the Geiger counter detects the radioactive material decaying — better known as radioactivity — the hammer will smash the flask of poison and kill the cat. For the thought experiment, the probability of the material decaying is equal to the probability that it won’t decay.
According to an interpretation of quantum mechanics known as the Copenhagen interpretation, a subatomic particle can exist simultaneously in two quantum states and two places at once until it’s observed. But there was no proper fact or proof to make this interpretation a reality. Therefore, Schrödinger conducted this experiment of cat and concluded that the cat is, in a sense, both alive and dead while hidden in the box. The cat’s state is only resolved when an observer looks inside. Which is nothing but the Quantum Superposition as defined earlier.
Want to dive more deep into Quantum Cryptography ? Here are some of the sources and references I would suggest:
http://www.ucci.it/docs/QC-Pros+Cons-0.4.pdf
https://www.cse.wustl.edu/~jain/cse571-07/ftp/quantum/
https://homepage.univie.ac.at/Reinhold.Bertlmann/pdfs/dipl_diss/PetraPajic_BA_QuantumCryptography.pdf
http://www7b.biglobe.ne.jp/~kcy05t/index.html
http://www.didaktik.physik.uni-erlangen.de/quantumlab/english/index.html?/quantumlab/english/cryptography/V-QCD/index.html
https://www.slideshare.net/asertseminar/quantum-cryptography-33033373
https://www.tutorialspoint.com/cryptography/index.htm
If there is anything I have interpreted wrongly, please do correct me so that we can together make it meaningful.
If there is anything you would add more to this information, please be open to making this information worthwhile, useful, and better.
If there is any concern with this article, please let me know so that we can do the needful.
If there is anything fascinating you want me to know, please involve me in it. Peace!! 😊
