The contest between code-makers and code-breakers has been going on for thousands of years. The purpose of cryptography is to transmit information in such a way that access to it is restricted entirely to the intended recipient, even if the transmission itself is received by others. Key Distribution is the main problem in conventional cryptography. Recently, quantum mechanics has made a remarkable entry in this field in the form of Quantum cryptography in which key distribution is done by using laws of physics. This paper briefly discusses about conventional cryptography.
This paper also discusses about the fundamentals of quantum cryptography and illustrates its working and discusses its applications and implementations. Quantum cryptography not only ensures secure communication (privacy through uncertainty) but also detects eavesdropper’s presence. This science is of increasing importance with the advent of broadcast and network communication, such as electronic transactions, the Internet, e-mail, and cell phones etc. Within few years this technique would start encrypting some of the most valuable secrets of government and industry.
BACKGROUND:- The concept of cryptography dates back as far as the Roman Empire (Julius Cesar). Before the digital age this was widely used by the governments, especially for the military purposes.
IT’S IMPORTANCE :- Today this science is of Increasing importance with the advent of broadcast and network communication, such as business transactions, the Internet, e-mail, and mobile phones, where sensitive monetary, business, political, and personal communications are transmitted Over public channels.
HOW IS IT DONE:- Cryptography operates by sender scrambling or encrypting the original message or plaintext in a systematic way that obscures its meaning. The encrypted message or ciphertext is transmitted and the receiver will recover message by unscrambling or decrypting the transmission. In Today’s modern---- Cryptography, the encryption algorithm itself is public information and the security lies on the users’ knowledge of a secret string of information, known as the ‘key’. Everyone one can make copies of the encrypted message, but only the intended Recipient who possesses the correct key can unlock from it the original message.
SECRET KEY ENCRYPTION:- Also referred to as ‘Symmetric key Encryption’. In, Symmetric-key encryption each computer has a secret key (code). Symmetric-key requires that you know which computers will be talking to each other so you can install the key on each one. Symmetric-key encryption is essentially the same as a secret code that each of the two computers must know in order to decode the information. The code provides the key to decoding the message. A k-bit "secret key" is shared by two users. To make unauthorized decipherment more difficult, the transformation algorithm can be carefully designed to make each bit of output depend on every bit of the input. With such an arrangement, a key of 128 bits used for encoding results in a choice of about 1038 numbers. Eg: DES, 3-DES, RC4, RC5 etc
Disadvantages:-
PUBLIC KEY ENCRYPTION:- Public key encryption uses a combination of a private key and a public key. The private key is known only to your computer, while the public key is given by your computer to any computer that wants to communicate securely with it. To decode an encrypted message, a computer must use the public key, provided by the originating computer, and its own private key. Eg: RSA, ECC.
Disadvantages:-
RSA:-The widely used RSA algorithm is one example of PKC. Anyone wanting to receive a message publishes a key, which contains two numbers. A sender converts a message into a series of digits, and performs a simple mathematical calculation on the series using the publicly available numbers. Messages are deciphered by the recipient by performing another operation, known only to him.
Please refer for a more detailed study on various types of Cryptographic Algorithms
One proposed method for solving this key distribution problem is the appointment of a central key distribution server. Every potential communicating party registers with the server and establishes a secret key. The server then relays secure communications between users, but the server itself is vulnerable to attack. Here Quantum cryptography comes into play. Quantum encryption, provides a way of agreeing on a secret key without making this assumption.
Communication at the quantum level changes many of the conventions of both classical secret key and public key communication described above. For example, it is not necessarily possible for messages to be perfectly copied by anyone with access to them, nor for messages to be relayed without changing them in some respect, nor for an eavesdropper to passively monitor communications without being detected .
Hiesenberg’s uncertainty principle:- “The mere act of observing or measuring a particle will ultimately change its behaviour.” The essence of the uncertainty principle of quantum mechanics is twofold. First, any measurements made on a physical system that extracts some information about that system will necessarily disturb that system, albeit possibly in a very small way. Second, any measurement made on a physical system that extracts some information about a certain quantity, call it x, necessarily precludes obtaining information about a conjugate quantity of the same system, call it p.
Polarization by a filter: Unpolarized light enters a vertically aligned filter, which absorbs some of the light and polarizes the remainder in the vertical direction. A second filter tilted at some angle q absorbs some of the polarized light and transmits the rest, giving it a new polarization.
Working:- If a sender, typically designated Alice in the literature, uses a filter in the 0-deg/90-deg basis to give the photon an initial polarization (either horizontal or vertical, but she doesn't reveal which), a receiver Bob can determine this by using a filter aligned to the same basis. However if Bob uses a filter in the 45-deg/135-deg basis to measure the photon, he cannot determine any information about the initial polarization of the photon.
Alice and Bob are equipped with two polarizers each, one aligned with the rectilinear 0-deg/90-deg (or +) basis that will emit - or | polarized photons and one aligned with the diagonal 45-deg/135-deg (or X) basis that will emit \ or / polarized photons. Alice and Bob can communicate via a quantum channel over which Alice can send photons, and a public channel over which they can discuss results. An eavesdropper Eve is assumed to have unlimited computing power and access to both these channels, though she cannot alter messages on the public channel .
Alice begins to send photons to Bob, each one polarized at random in one of the four directions: 0, 45, 90, or 135 deg. As Bob receives each photon, he measures it with one of his polarizers chosen at random. Since he does not know which direction Alice chose for her polarizer, his choice may not match hers. If it does match the basis, Bob will measure the same polarization as Alice sent, but if it doesn't match, Bob's measurement will be completely random. For instance, if Alice sends a photon | and Bob measures with his + polarizer oriented either - or |, he will correctly deduce Alice sent a | photon, but if he measures with his X polarizer, he will deduce (with equal probability) either \ or /, neither of which is what Alice actually sent. Furthermore, his measurement will have destroyed the original polarization.
To eliminate the false measurements from the sequence, Alice and Bob begin a public discussion after the entire sequence of photons has been sent. Bob tells Alice which basis he used to measure each photon, and Alice tells him whether or not it was the correct one. Neither Alice nor Bob announces the actual measurements, only the bases in which they were made. They discard all data for which their polarizers didn't match, leaving (in theory) two perfectly matching strings. They can then convert these into bit strings by agreeing on which photon directions should be 0 and which should be 1.
These characteristics provide the principles behind quantum cryptography. If an eavesdropper Eve uses a filter aligned with Alice's filter, she can recover the original polarization of the photon. But if she uses a misaligned filter she will not only receive no information, but will have influenced the original photon so that she will be unable to reliably retransmit one with the original polarization. Bob will either receive no message or a garbled one, and in either case will be able to deduce Eve's presence. A user can suggest a key by sending a series of photons with random polarizations.
This sequence can then be used to generate a sequence of numbers. The process is known as quantum key distribution. If the key is intercepted by an eavesdropper, this can be detected and it is of no consequence, since it is only a set of random bits and can be discarded. The sender can then transmit another key. Once a key has been securely received, it can be used to encrypt a message that can be transmitted by conventional means: telephone, e-mail, or regular postal mail
This paper also discusses about the fundamentals of quantum cryptography and illustrates its working and discusses its applications and implementations. Quantum cryptography not only ensures secure communication (privacy through uncertainty) but also detects eavesdropper’s presence. This science is of increasing importance with the advent of broadcast and network communication, such as electronic transactions, the Internet, e-mail, and cell phones etc. Within few years this technique would start encrypting some of the most valuable secrets of government and industry.
Introduction:-
WHAT IS CRYPTOGRAPHY:-cryptography is a science whose purpose is to transmit information in such a way that access to it is restricted entirely to the intended recipient, even if the transmission itself is received by others.BACKGROUND:- The concept of cryptography dates back as far as the Roman Empire (Julius Cesar). Before the digital age this was widely used by the governments, especially for the military purposes.
IT’S IMPORTANCE :- Today this science is of Increasing importance with the advent of broadcast and network communication, such as business transactions, the Internet, e-mail, and mobile phones, where sensitive monetary, business, political, and personal communications are transmitted Over public channels.
HOW IS IT DONE:- Cryptography operates by sender scrambling or encrypting the original message or plaintext in a systematic way that obscures its meaning. The encrypted message or ciphertext is transmitted and the receiver will recover message by unscrambling or decrypting the transmission. In Today’s modern---- Cryptography, the encryption algorithm itself is public information and the security lies on the users’ knowledge of a secret string of information, known as the ‘key’. Everyone one can make copies of the encrypted message, but only the intended Recipient who possesses the correct key can unlock from it the original message.
Conventional Cryptography:-
Existing cryptographic techniques are usually identified as "traditional" or "modern."- Traditional techniques date back for centuries, and use operations of coding (use of alternative words or phrases), transposition (reordering of plaintext), and substitution (alteration of plaintext characters). Traditional techniques were designed to be simple, for hand encoding and decoding. By contrast, modern techniques use computers, and rely on extremely long keys, convoluted algorithms, and intractable problems to achieve assurances of security.
- Most computer encryption systems (Modern) belong in one of two categories:
- Secret-key encryption
- Public-key encryption
SECRET KEY ENCRYPTION:- Also referred to as ‘Symmetric key Encryption’. In, Symmetric-key encryption each computer has a secret key (code). Symmetric-key requires that you know which computers will be talking to each other so you can install the key on each one. Symmetric-key encryption is essentially the same as a secret code that each of the two computers must know in order to decode the information. The code provides the key to decoding the message. A k-bit "secret key" is shared by two users. To make unauthorized decipherment more difficult, the transformation algorithm can be carefully designed to make each bit of output depend on every bit of the input. With such an arrangement, a key of 128 bits used for encoding results in a choice of about 1038 numbers. Eg: DES, 3-DES, RC4, RC5 etc
Disadvantages:-
- A large bit key is required for secure communication.
- The key is subject to interception by hackers.
PUBLIC KEY ENCRYPTION:- Public key encryption uses a combination of a private key and a public key. The private key is known only to your computer, while the public key is given by your computer to any computer that wants to communicate securely with it. To decode an encrypted message, a computer must use the public key, provided by the originating computer, and its own private key. Eg: RSA, ECC.
Disadvantages:-
- Much slower compared to secret key encryption.
- Ciphertext is much larger than the plaintext.
RSA:-The widely used RSA algorithm is one example of PKC. Anyone wanting to receive a message publishes a key, which contains two numbers. A sender converts a message into a series of digits, and performs a simple mathematical calculation on the series using the publicly available numbers. Messages are deciphered by the recipient by performing another operation, known only to him.
Please refer for a more detailed study on various types of Cryptographic Algorithms
Key Distribution Problem:-
The main practical problem with secret key encryption is exchanging a secret key. In principle any two users who wished to communicate could first meet to agree on a key in advance, but in practice this could be inconvenient. Other methods for establishing a key, such as the use of secure courier or private knowledge, could be impractical for routine communication between many users. But any discussion of how the key is to be chosen that takes place on a public communication channel could in principle be intercepted and used by an eavesdropper.One proposed method for solving this key distribution problem is the appointment of a central key distribution server. Every potential communicating party registers with the server and establishes a secret key. The server then relays secure communications between users, but the server itself is vulnerable to attack. Here Quantum cryptography comes into play. Quantum encryption, provides a way of agreeing on a secret key without making this assumption.
Communication at the quantum level changes many of the conventions of both classical secret key and public key communication described above. For example, it is not necessarily possible for messages to be perfectly copied by anyone with access to them, nor for messages to be relayed without changing them in some respect, nor for an eavesdropper to passively monitor communications without being detected .
INTRODUCTION TO QUANTUM CRYPTOGRAPHY:-
Quantum cryptography is a new field based on quantum mechanics A quantum cryptography system is a key distribution system that attempts to link the security of the system to the correctness of the uncertainty principle of quantum mechanicsHiesenberg’s uncertainty principle:- “The mere act of observing or measuring a particle will ultimately change its behaviour.” The essence of the uncertainty principle of quantum mechanics is twofold. First, any measurements made on a physical system that extracts some information about that system will necessarily disturb that system, albeit possibly in a very small way. Second, any measurement made on a physical system that extracts some information about a certain quantity, call it x, necessarily precludes obtaining information about a conjugate quantity of the same system, call it p.
FUNDAMENTALS OF QUANTUM CRYPTOGRAPHY:-
To understand the ideas of Quantum Cryptography, we must first discuss some underlying physics.
- Electromagnetic waves such as light waves can exhibit the phenomenon of polarization, in which the direction of the electric field vibrations is constant or varies in some definite way. A polarization filter is a material that allows only light of a specified polarization direction to pass. If the light is randomly polarized, only half of it will pass a perfect filter.
- According to quantum theory, light waves are propagated as discrete particles known as photons. A photon is a massless particle, the quantum of the electromagnetic field, carrying energy, momentum, and angular momentum. The polarization of the light is carried by the direction of the angular momentum or spin of the photons. A photon either will or will not pass through a polarization filter, but if it emerges it will be aligned with the filter regardless of its initial state; there are no partial photons.
- The foundation of quantum cryptography lies in the Heisenberg uncertainty principle, which states that certain pairs of physical properties are related in such a way that measuring one property prevents the observer from simultaneously knowing the value of the other. In particular, when measuring the polarization of a photon, the choice of what direction to measure affects all subsequent measurements. For instance, if one measures the polarization of a photon by noting that it passes through a vertically oriented filter, the photon emerges as vertically polarized regardless of its initial direction of polarization. If one places a second filter oriented at some angle q to the vertical, there is a certain probability that the photon will pass through the second filter as well, and this probability depends on the angle q. As q increases, the probability of the photon passing through the second filter decreases until it reaches 0 at q = 90 deg (i.e., the second filter is horizontal). When q = 45 deg, the chance of the photon passing through the second filter is precisely 1/2. This is the same result as a stream of randomly polarized photons impinging on the second filter, so the first filter is said to randomize the measurements of the second.
Polarization by a filter: Unpolarized light enters a vertically aligned filter, which absorbs some of the light and polarizes the remainder in the vertical direction. A second filter tilted at some angle q absorbs some of the polarized light and transmits the rest, giving it a new polarization.
- A pair of orthogonal (perpendicular) polarization states used to describe the polarization of photons, such as horizontal/vertical, is referred to as a basis. A pair of bases are said to be conjugate bases if the measurement of the polarization in the first basis completely randomizes the measurement in the second basis , as in the above example with q = 45 deg. It is a fundamental consequence of the Heisenberg uncertainty principle that such conjugate pairs of states must exist for a quantum system.
Working:- If a sender, typically designated Alice in the literature, uses a filter in the 0-deg/90-deg basis to give the photon an initial polarization (either horizontal or vertical, but she doesn't reveal which), a receiver Bob can determine this by using a filter aligned to the same basis. However if Bob uses a filter in the 45-deg/135-deg basis to measure the photon, he cannot determine any information about the initial polarization of the photon.
Alice and Bob are equipped with two polarizers each, one aligned with the rectilinear 0-deg/90-deg (or +) basis that will emit - or | polarized photons and one aligned with the diagonal 45-deg/135-deg (or X) basis that will emit \ or / polarized photons. Alice and Bob can communicate via a quantum channel over which Alice can send photons, and a public channel over which they can discuss results. An eavesdropper Eve is assumed to have unlimited computing power and access to both these channels, though she cannot alter messages on the public channel .
Alice begins to send photons to Bob, each one polarized at random in one of the four directions: 0, 45, 90, or 135 deg. As Bob receives each photon, he measures it with one of his polarizers chosen at random. Since he does not know which direction Alice chose for her polarizer, his choice may not match hers. If it does match the basis, Bob will measure the same polarization as Alice sent, but if it doesn't match, Bob's measurement will be completely random. For instance, if Alice sends a photon | and Bob measures with his + polarizer oriented either - or |, he will correctly deduce Alice sent a | photon, but if he measures with his X polarizer, he will deduce (with equal probability) either \ or /, neither of which is what Alice actually sent. Furthermore, his measurement will have destroyed the original polarization.
To eliminate the false measurements from the sequence, Alice and Bob begin a public discussion after the entire sequence of photons has been sent. Bob tells Alice which basis he used to measure each photon, and Alice tells him whether or not it was the correct one. Neither Alice nor Bob announces the actual measurements, only the bases in which they were made. They discard all data for which their polarizers didn't match, leaving (in theory) two perfectly matching strings. They can then convert these into bit strings by agreeing on which photon directions should be 0 and which should be 1.
These characteristics provide the principles behind quantum cryptography. If an eavesdropper Eve uses a filter aligned with Alice's filter, she can recover the original polarization of the photon. But if she uses a misaligned filter she will not only receive no information, but will have influenced the original photon so that she will be unable to reliably retransmit one with the original polarization. Bob will either receive no message or a garbled one, and in either case will be able to deduce Eve's presence. A user can suggest a key by sending a series of photons with random polarizations.
This sequence can then be used to generate a sequence of numbers. The process is known as quantum key distribution. If the key is intercepted by an eavesdropper, this can be detected and it is of no consequence, since it is only a set of random bits and can be discarded. The sender can then transmit another key. Once a key has been securely received, it can be used to encrypt a message that can be transmitted by conventional means: telephone, e-mail, or regular postal mail
Illustration of Quantum Key Distribution:-
A quantum cryptography system allows two people; say Alice and Bob, to exchange a secret key. Alice uses a transmitter to send photons in one of four polarizations: 0, 45, 90 or 135 degrees. Bob uses a receiver to measure each polarization in either the rectilinear basis (0 and 90) or the diagonal basis (45 and 135). 
The BB84 system is now one of several types of quantum cryptosystems for key distribution. The basic idea of those cryptosystems is as follows. A sequence of correlated particle pairs is generated, with one member of each pair being detected by each party. An eavesdropper on this communication would have to detect a particle to read the signal, and retransmit it in order for his presence to remain unknown. However, the act of detection of one particle of a pair destroys its quantum correlation with the other, and the two parties can easily verify whether this has been done, without revealing the results of their own measurements, by communication over an open channel.
Quantum Cryptography Applications:-
- The genius of quantum cryptography is that it solves the problem of key distribution Sending a message using photons is straightforward in principle, since one of their quantum properties, namely polarization, can be used to represent a 0 or a 1. Each photon therefore carries one bit of quantum information, which physicists call a qubit. The sender and receiver can easily spot the alterations by the measurements caused by the eavesdropper. Cryptographers cannot exploit this idea to send private messages, but they can determine whether its security was compromised in retrospect.
- Provides absolute security where it is needed. For example:
- Financial institutions and trading exchanges :- QKD can secure most critical communications
- Ultra secure point-to-point links :- Generally where a high secure point-to-point communication is needed
- Using these principles research is being done for high-speed free-space and fiber-optic quantum cryptography implemented via ground-ground, ground-satellite, aircraft-satellite and satellite-satellite links.
Drawbacks:-
- Distance is limited to only tens of kilometers
- Since Optical fibres are used to transmit photons; losses occur along the fibre
- Amplifiers cannot be used as they destroy the qubit state.
Conclusion:-
Quantum cryptography promises to revolutionize secure communication by providing security based on the fundamental laws of physics, instead of the current state of mathematical algorithms or computing technology.
The advantage of quantum cryptography over traditional key exchange methods is that the exchange of information can be shown to be secure in a very strong sense, without making assumptions about the intractability of certain mathematical problems. The devices for implementing such methods exist and the performance of demonstration systems is being continuously improved.
Within the next few years, if not months, such systems could start encrypting some of the most valuable secrets of government and industry.
References:-
- Herbert Goldstein "Classical Mechanics".
- Wher, Richards and Adair "physics of the atom" fourth edition.
- James F. Kurose and Keith W. Ross "Computer networking" second edition. A top down approach featuring the internet.
- Bruce Schneier "Applied Cryptography" second edition. Protocols, Algorithms and source code in C.
- Salvatore Vittorio “Quantum Cryptography: Privacy through Uncertainty" (Released October 2002)
- Quantum Cryptography Tutorial by James Ford.
- Text by Artur Ekert last update March 20, 1995 by K-A S. "CQC Introductions: Quantum Cryptography"
- Wikipedia, the free encyclopedia "Quantum cryptography".
- Michel Gualtieri (April 2000) "A Quantum twist on decoding and encoding". Seton Hall University- computer science undergraduate program.
Technical Paper on Quantum Cryptography
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