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Cryptography in the quantum world

Claude Crépeau

Published Jan 20, 2003• 1 citation
Publisher

Abstract

We survey a number of results concerning transmission of quantum information secretly. First of all, we present the basic concepts of quantum information and the rules guiding it. Then we consider quantum teleportation which is the quantum equivalent of the classical one-time-pad, showing the possibility of transmission of perfectly secret quantum messages as long as the users have exchanged a (quantum) secret key before end of a special Einstein-Podolsky-Rosen type. Then we consider quantum cryptography, a technique used to secretly exchange a cryptographic key using the uncertainty principle to determine the amount of tempering on the communication. We unveil a technique known as entanglement purification that publicly allows amplification of the privacy of a random secret key. Combined with quantum cryptography this technique allows users to exchange EPR particles publicly and purify them after tempering of an adversary in order to transmit secret information through teleportation. Finally, the quantum equivalent of Shamir's secret sharing is presented.

DOI
10.1109/itnw.1999.814350

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Users of communication channels wish to have their transactions secured. Therefore, it is necessary to develop techniques which can ensure that eavesdroppers cannot intercept the messages transmitted. The technology concerned with the secure communication of data is termed as cryptography [1-3]. It is the art of hiding information in the form of a string of bits to an unauthorized party. To achieve this goal, in a classical cryptography system the message bits are combined with random bits of equal length called a key. The combined data is known as cryptogram. This technique is called encryption. A key can be public or private. The public key is to encode plaintext, while the private key is for decoding the previously encoded plaintext or cryptogram. The cryptogram is generally sent through the communication channel. Because of the randomness of the key the encoded message is completely random. Consequently, the message is untraceable to an eavesdropper. The safety of the transmission completely depends on the safety of the key. Therefore, the key should be kept secret by the users.
When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a communications channel on which it is impossible in principle to eavesdrop without a high probability of disturbing the transmission in such a way as to be detected. Such a quantum channel can be used in conjunction with ordinary insecure classical channels to distribute random key information between two users with the assurance that it remains unknown to anyone else, even when the users share no secret information initially. We also present a protocol for coin-tossing by exchange of quantum messages, which is secure against traditional kinds of cheating, even by an opponent with unlimited computing power, but ironically can be subverted by use of a still subtler quantum phenomenon, the Einstein-Podolsky-Rosen paradox.
Quantum Cryptography is based on the use of subatomic particles (photons) and their intrinsic quantum properties (photon polarization) to develop an unbreakable system. It is not possible to measure the quantum state of any system without affecting the system. This property provides secure transmission of key between sender and receiver. Quantum Cryptography is a way to combine the relative ease and convenience of key exchange in public key cryptography with the ultimate security of a one-time pad. Quantum techniques for key distribution, the classically impossible task of distributing secret information over an insecure channel whose transmissions are subject to inspection by an eavesdropper, between parties who share no secret key initially. Quantum Cryptography uses the principles of Quantum Mechanics to implement a cryptographic system. The key problem which is solved by using quantum techniques is that of eavesdropping detection. The bits are represented as qubits, physically modeled by photons, and communicated over a quantum channel. The polarization states of photons represent 0's and 1's. Keyword: Asymmetric key, Cryptography, Protocols, Quantum, symmetric key
Quantum computing and quantum cryptography are two areas of research that have the potential to transform modern computing and communication. Quantum computing promises to solve computational problems that are beyond the reach of classical computers, while quantum cryptography provides a way to secure communication channels that is immune to eavesdropping. Quantum cryptography is one of the emerging topics in the field of computer industry. This article focuses on quantum cryptography and how this technology makes a valuable contribution to an intensive defense strategy of completely secure key distribution. The scope of this article covers the weaknesses of modern digital cryptographic systems, the basic concepts of quantum cryptography, the practical implementations of this technology, and its limitations. , and finally the future direction that quantum cryptography is headed. We describe the result of an apparatus and protocol designed to perform quantum key distribution, whereby two users do not share any secret information (no private or public keys are known). previously known) initially exchanges a random quantum transmission consisting of veryweakly polarized light rays. In particular, readers can explore the following topics in depth: current cryptographic schemes (symmetric and asymmetric), the difference between quantum and classical computing, challenges of quantum computing, quantum algorithms (Shor and Grover), public key cryptographic schemes affected, symmetry affected schemes, impact on hash functions and post-quantum cryptography
The application of internet has spiked up in the present-day scenario, as the exchange of information made between two parties happens in public environment. Hence privacy of information plays an important role in our day to day life. There have been incredible developments made in the field of cryptography resulting in modern cryptography at its zenith. Quantum computers are one among them creating fear into security agencies across the world. Solving the complex mathematical calculations is uncomplicated using quantum computers which results in breaking the keys of modern cryptography, which cannot be broken using classical computers. The concept of quantum physics, into the cryptographic world has resulted in the advancement of quantum cryptography. This technique utilizes the idea of key generation by photons, and communicates between peer entities by secured channel. Quantum cryptography adapts quantum mechanical principles like Heisenberg Uncertainty principle and photon polarization principle to provide secure communication between two parties. This article focuses on generation of a secret shared key, later converted into Quantum bits (Qbits) and transmitted to the receiver securely.
Quantum cryptography provides secret communication, which offers various security factors like confidentiality, integrity, and authentication assurance based on the law of physics. The law of physics states that quantum computing can also be applied into the communication sector, which is particularly in the field of cryptography. Then quantum can significantly distribute the data securely by applying quantum key distribution (QKD), quantum key sharing, etc. In the classical cryptography, it is difficult to compute secret keys using security concepts like key exchange and authentication, etc., and it fails to provide adequate protection during data communication as it needs some effective computation in terms of security. The lack of security in the data communication can be overcome by using the concept of quantum computing. Generally, in quantum computing, elementary quantum systems like polarized photons are used to transmit digital information based on the principle of uncertainty as it gives rise to a significant phenomenon of effective security in terms of communication compared to existing concepts related to cryptography. In quantum computing, the detection ratio for identifying the data which are sent through a communication channel is more difficult as it uses qubits and photons to represent the data that are sent. Quantum channels are used to distribute the information between two users as it passes through the unprotected classical channels as it is unknown to anyone else. Assuming that Alice and Bob use a latent noise channel to send a key, reconciliation is the process of correcting errors between Alice and Bob’s version of the key. This is done by public discussion, which leaks some information about the secret key to an undercover. This chapter gives a discussion on QKD concepts as it helps to provide a secure communication, where the information is broadcasting through a quantum channel. Finally, the various existing quantum protocols are described in relation to some security measures based on QKD, and the standard QKD protocol of BB84 is discussed.