Analysis Of Quantum Cryptography Communications Essay

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Cryptography is the science of keeping private information from unauthorized access, of ensuring data integrity and authentication, and other tasks. In this survey, we will focus on quantum-cryptographic key distribution and bit commitment protocols and we in particular will discuss their security. Before turning to quantum cryptography, let me give a brief review of classical cryptography, its current challenges and its historical development.

Two parties, Alice and Bob, wish to exchange messages via some insecure channel in a way that protects their messages from eavesdropping. An algorithm, which is called a cipher in this context, scrambles Alice's message via some rule such that restoring the original message is hard-if not impossible-without knowledge of the secret key. This “scrambled” message is called the cipher text. On the other hand, Bob (who possesses the secret key) can easily decipher Alice's cipher text and obtains her original plaintext. Fig 1.1 in this section presents this basic cryptographic scenario.

Communication between Alice and Bob, with Eve listening

Alice's random bit

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Alice's random sending basis

Photon polarization Alice sends

Bob's random measuring basis

Photon polarization Bob measures

PUBLIC DISCUSSION OF BASIS

Shared secret key

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To check for the presence of eavesdropping Alice and Bob now compare a certain subset of their remaining bit strings. If a third party (usually referred to as Eve, for 'eavesdropper') has gained any information about the photons' polarization, this will have introduced errors in Bobs' measurements. If more than p bits differ they abort the key and try again, possibly with a different quantum channel, as the security of the key cannot be guaranteed. p is chosen so that if the number of bits known to Eve is less than this, privacy amplification can be used to reduce Eve's knowledge of the key to an arbitrarily small amount, by reducing the length of the key.

2. HISTORY OF QUANTUM CRYPTOGRAPHY

Quantum cryptography was proposed first by Stephen Wiesner, and then at Columbia University in New York, who, in the early 1970s, introduced the concept of quantum conjugate coding. His seminal paper titled "Conjugate Coding" was rejected by IEEE Information Theory but was eventually published in 1983 in SIGACT News (15:1 pp. 78-88, 1983). In this paper he showed how to store or transmit two messages by encoding them in two “conjugate observables”, such as linear and circular polarization of light, so that either, but not both, of which may be received and decoded. He illustrated his idea with a design of unforgivable bank notes. A decade later, building upon this work, Charles H. Bennett, of the IBM Thomas J. Watson Research Center, and Gilles Brassard, of the Universities de Montréal, proposed a method for secure communication based on Wiesner's “conjugate observables”. In 1990, independently and initially unaware of the earlier work, Artur Ekert, then a Ph.D. student at Wolfson College, University of Oxford, developed a different approach to quantum cryptography based on peculiar quantum correlations known as quantum entanglement.

3. CLASSICAL CRYPTOGRAPHY

We present just the basic definition of a cryptosystem and give one example of a classical encryption method, the one-time pad.

3.1 DEFINITION OF CRYPTOSYSTEM

A (deterministic, symmetric) cryptosystem is a five-tipple (P, C, K, E, D) satisfying the following conditions:

  1. P is a finite set of possible plaintexts.
  2. C is a finite set of possible cipher texts.
  3. K is a finite set of possible keys.
  4. For each k є K, there are an encryption rule ek є E and a corresponding decryption rule dk є D, where ek: P→ C and dk: C→ P are functions satisfying dk (ek (x)) = x for each plaintext element x є P.

In the basic scenario in cryptography, we have two parties who wish to communicate over an insecure channel, such as a phone line or a computer network. Usually, these parties are referred to as Alice and Bob. Since the communication channel is insecure, an eavesdropper, called Eve, may intercept the messages that are sent over this channel. By agreeing on a secret key k via a secure communication method, Alice and Bob can make use of a cryptosystem to keep their information secret, even when sent over the insecure channel. This situation is illustrated in Fig 1.1.

The method of encryption works as follows. For her secret message m, Alice uses the key k and the encryption rule ek to obtain the cipher text c = ek (m). She sends Bob the cipher text c over the insecure channel. Knowing the key k, Bob can easily decrypt the cipher text by the decryption rule dk: dk (c) = dk (ek (m)) = m. Knowing the cipher text c but missing the key k, there is no easy way for Eve to determine the original message m. There exist many cryptosystems in modern cryptography to transmit secret messages. An early well-known system is the one-time pad, which is also known as the Vernam cipher. The one-time pad is a substitution cipher. Despite its advantageous properties, which we will discuss later on, the one-time pad's drawback is the costly effort needed to transmit and store the secret keys.

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Fig.3.1 Letters and punctuation marks encoded by numbers from 0 to 29

3.2 ONE-TIME PAD

For plaintext elements in P, we use capital letters and some punctuation marks, which we encode as numbers ranging from 0 to 29, see Fig.3.2.

As is the case with most cryptosystems, the cipher text space equals the plaintext space. The key space K also equals P, and we have P =C= K= {0, 1 . . . 29}. Next, we describe how Alice and Bob use the one-time pad to transmit their messages. A concrete example is shown in Fig.3.2. Suppose Alice and Bob share a joint secret keykof length n= 12, where each key symbol kie {0, 1 . . . 29} is chosen uniformly at random. Let m= m1m2. . .mn be a given message of length n, which Alice wishes to encrypt. For each plaintext letter mi, where 1 ≤ i≤ n, Alice adds the plaintext numbers to the key numbers. The result is taken modulo 30. For example, the last letter of the plaintext from Fig.3.2, “D,” is encoded by “m12=03.” The corresponding key is “m12= 28,” so we have c12= 3 + 28 = 31. Since 31 ≡ 1 mod 30, our plaintext letter “D” is encrypted as “B.”

Decryption works similarly by subtracting, character by character, the key letters from the corresponding cipher text letters. So the encryption and decryption can be written as respectively ci= (mi+ ki) mod 30 and mi= (ci− ki) mod 30, 1 ≤ i ≤ n.

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Fig.3.2 Encryption and decryption example for the one time pad

3.3. PROTOCOLS OF QKD

  1. BB84 (and DARPA Project) - uses polarization of photons to encode the bits of information - relies on “uncertainty” to keep Eve from learning the secret key.
  2. Ekert - uses entangled photon states to encode the bits - relies on the fact that the information defining the key only "comes into being" after measurements performed by Alice and Bob.

3.4. LIMITATIONS

Cryptographic technology in use today relies on the hardness of certain mathematical problems. Classical cryptography faces the following two problems which are as follows.

  1. The security of many classical cryptosystems is based on the hardness of problems such as integer factoring or the discrete logarithm problem. But since these problems typically are not probablyhard, the corresponding cryptosystems are potentially insecure.
  2. The theory of quantum computation has yielded new methods to tackle these mathematical problems in a much more efficient way. Although there are still numerous challenges to overcome before a working quantum computer of sufficient power can be built, in theory many classical ciphers might be broken by such a powerful machine.

However, while quantum computation seems to be a severe challenge to classical cryptography in a possibly not so distant future, at the same time it offers new possibilities to build encryption methods that are safe even against attacks performed by means of a quantum computer. Quantum cryptography extends the power of classical cryptography by protecting the secrecy of messages using the physical laws of quantum mechanics.

4. QUANTUM CRYPTOGRAPHY

Quantum Cryptography, or Quantum Key Distribution (QKD), uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random bit string known only to them, which can be used as a key to encrypt and decrypt messages. An important and unique property of quantum cryptography is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This result from a fundamental part of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superposition's or quantum entanglement and transmitting information in quantum states, a communication system can be implemented which detects eavesdropping. If the level of eavesdropping is below a certain threshold a key can be produced which is guaranteed as secure (i.e. the eavesdropper has no information about), otherwise no secure key is possible and communication is aborted. The security of quantum cryptography relies on the foundations of quantum mechanics, in contrast to traditional public key cryptography which relies on the computational difficulty of certain mathematical functions, and cannot provide any indication of eavesdropping or guarantee of key security. Quantum cryptography is only used to produce and distribute a key, not to transmit any message data. This key can then be used with any chosen encryption algorithm to encrypt (and decrypt) a message, which can then be transmitted over a standard communication channel. The algorithm most commonly associated with QKD is the one-time pad, as it is provably secure when used with a secret, random key. Quantum cryptography exploits the quantum mechanical property that a qubit cannot be copied or amplified without disturbing its original state. This is the statement of the No-Cloning Theorem [Wootters and Zurek 1982]. The essence of this theorem is the main ingredient of quantum key channel to exchange a sequence of qubits, which will then be used to create a key for the one-time pad in order to communicate over an insecure channel. Any disturbance of the qubits, for example caused by Eve trying to measure the qubits' state, can be detected with high probability. Quantum cryptographic devices typically employ individual photons of light and take advantage of either the Heisenberg Uncertainty principle or Quantum Entanglement.

5. CRYPTOGRAPHIC PROTOCOLS

Cryptographic protocols (especially such primitive ones as BC (bit commitment) and OT (Oblivious transfer) are almost never executed on their own. They are usually used as building blocks of more complex applications.

  1. It is already known that composition of secure protocols does not have to be secure.
  2. Cryptographic protocols are algorithms for two or more parties how to conduct communication/cooperation in such a way that certain cryptographic goals are achieved (security, secrecy, anonymity, . . .) - even if a certain number of parties are malicious (may cheat).
  3. Oblivious transfer, 1-out-of-2 oblivious transfer, bit commitment and (long-distance) coin-tossing are main primitives of cryptographic protocols.
  4. Using oblivious transfer one can implement securely bit commitment and using bit commitment one can implement coin-tossing protocol.
  5. Using oblivious transfer one can implement securely any multiparty computation at which each party keep secret its inputs

6. BASIC PRIMITIVES OF QUANTUM CRYPTOGRAPHY

Quantum cryptography has some primitives in their own progressive field which are explained as follows.

  1. Quantum one-time pad and its generalizations via private channels and randomization.
  2. Quantum variations on coin tossing bit commitment and oblivious transfer protocols.
  3. Quantum variations on zero-knowledge protocols.
  4. Identification and authentication protocols
  5. Quantum protocols to share and hide classical and quantum information
  6. Anonymity protocols

7. CRYPTOGRAPHIC SYSTEM

Recent quantum cryptosystems have concentrated on using optical fibers to transmit the photons. In March of this year a Swiss team of researchers successfully conducted a quantum key exchange over the telephone network between Geneva and Lausanne, a distance of 67 kilometers. In August last year in the US, a team based in Los Alamos, New Mexico, managed to transmit using two portable units across six miles of desert. The work at Los Alamos is geared towards eventually sending quantum-encrypted information from the ground to satellites, which would remove all limits to the distances over which communications could be secured.

8 IMPORTANCE OF SECURITY

Security is important in each and every field for preventing the data, information from any unauthorized dealing. The encryption and decryption is very common these days so for the protection of the information its security is a necessity. Different 4 eras in which the security can be explained are follows.

8.1 NEOLITHIC ERA

Progress was made on the basis that men learned how to make use of the potentials provided by the biological world to have food available in a sufficient amount and whenever needed.

8.2 INDUSTRIAL ERA

Progress has been made on the basis that men have learned how to make use of the laws and limitations of the physical world to have energyavailable in a sufficient amount and whenever needed.

8.3 INFORMATION ERA

Progress is and will be made on the basis that man learns how to make use of the laws and limitations of the information world to have information(processing energy) available in a sufficient amount and whenever needed.

8.4 SECURITY ERA

Progress is and will be made on the basis that man learns how to make use of the laws and limitations of the physical and information worlds to have security available in a sufficient amount and whenever needed.

9. SECURITY FROM QUANTUM CRYPTOGRAPHY

Various kinds of securities are offered by the quantum cryptography which is speeded in various fields. Main kinds of security offered by quantum cryptography can be explained by two forms as follows presence of enemies and in the presence of dishonest parties.

9.1 SECURITY IN THE PRESENCE OF ENEMIES

A variety of (external/enemy) attacks on cryptographic systems have been investigated so far. Some of main ones:

  1. Powerful Eve;
  2. Man-in-the-middle attacks
  3. Denial of services
  4. Attacks on physical systems in use - see attacks on the underlying technology in case of the RSA cryptosystems, a good theory of (quantum) attacks is needed.

9.2 SECURITY IN PRESENCE OF DISHONEST PARTIES

Securities are recommended at each and every place for the proper protection of the data from any unauthorized dealing. It is demand of every field that there information must have to be secure from dishonest parties various factors used for this are as follows.

  1. In case of multiparty protocols one of the key questions is to ask how many dishonest parties (cheaters) can be tolerated and how to achieve that.
  2. One of main result along this line (quant-ph/0801.1544) says that in the case multiparty quantum computations with n parties up to ⌊n−12 ⌋ cheaters can be tolerated by a universally compo sable protocol.
  3. In the same paper it has been shown that a verifiable quantum secret sharing is possible in the case of the same number ⌊n−12 ⌋ of cheaters.

10. THEORETICAL IMPORTANCE OF CRYPTOGRAPHY

Quantum cryptography has its own greater importance in the theoretical field which is explained as follows.

  1. Fundamental concepts of classical cryptography, and the corresponding laws and limitations, have turned out to be of the key importance for foundation of classical information processing - informatics.
  2. Fundamental concepts of quantum cryptography, and the corresponding laws and limitations, are expected to be of the key importance for foundation of quantum information processing and also informatics and (quantum) physics.

11. APPLICATIONS OF QUANTUM CRYPTOGRAPHY

Quantum cryptography systems are already used by some government agencies, large banks, telecommunications companies and other corporations who handle sensitive or military data. Commercial quantum cryptographic systems are available from a range of companies including MagiQ, id Quantique and NEC.

12. MAIN PROBLEMS/AREAS OF CRYPTOGRAPHY

The areas in which quantum cryptography has faced a lot of problems are as follows. These problems made difficult to exist but still has greater achievements in the co-existing world.

  1. Steganography and watermarking.
  2. Secret-key cryptography.
  3. Secret-key distribution/generation.
  4. Public-key cryptography (RSA Elliptic curves cryptography, McEllice cryptosystem).
  5. Digital signatures.
  6. Authentication.
  7. Anonymity.
  8. Privacy.

CONCLUSION AND FUTURE SCOPE

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 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. Future developments will focus on faster photon detectors, a major factor limiting the development of practical systems for widespread commercial use. The ultimate goal is to make QKD more reliable, integrate it with today's telecommunications infrastructure, and increase the transmission distance and rate of key generation. Thus the Long-term goals of quantum key distribution are the realistic implementation via fibers, for example, for different buildings of a bank or company, and free space key exchange via satellites. Quantum cryptography already provides the most advanced technology of quantum information science, and is on the way to achieve the (quantum) jump from university laboratories to the real world.

ACKNOWLEDGEMENT

I thank GODalmighty for guiding me throughout the term paper. I would like to thank all those who have contributed to the completion of the term paper and helped me with valuable suggestions for improvement. I am extremely grateful to Mr.DHANANJAY DEVANGAN, Department of ELECTRONICS AND COMMUNICATIONS,for providing me with best facilities and atmosphere for the creative work guidance and encouragement. I thank all my friends for extending their cooperation during my term paper. Above all I would like to thank my parents without whose blessings; I would not have been able to accomplish my goal.

REFERENCES

[1] www.yahoo.com (quantum challenges of cryptography for quantum information).

[2] www.google.com (quantum cryptography ppt.).

[3] www.wikipedia.com (quantum cryptography).

[4] www.google.com (Seminar Report on Quantum Cryptography by SANTHIMOL)

[5] www.google.com (applications of Quantum Cryptography).

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