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Physical Review A

Invisible transmission in quantum cryptography using continuous variables: A proof of Eve’s vulnerability

Patrick Navez, A. Gatti, Luigi A. Lugiato

Published Feb 13, 2002• 0 citations
Publisher

Abstract

By analogy to classical cryptography, we develop a quantum cryptographic scheme in which the two public and private keys consist in each of two entangled beams of squeezed light. An analog secret information is encrypted by modulating the phase of the beam sent in public. The knowledge of the degree of nonclassical correlation between the beam quadratures measured in private and in public allows only the receiver to decrypt the secret information. Finally, in a view towards absolute security, we formally prove that any external intervention of an eavesdropper makes him vulnerable to any subsequent detection.

DOI
10.1103/physreva.65.032307

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By analogy to classical cryptography, we develop a quantum cryptographic scheme in which the two public and private keys consist in each of two entangled beams of squeezed light. An analog secret information is encrypted by modulating the phase of the beam sent in public. The knowledge of the degree of nonclassical correlation between the beam quadratures measured in private and in public allows only the receiver to decrypt the secret information. Finally, in a view towards absolute security, we formally prove that any external intervention of an eavesdropper makes him vulnerable to any subsequent detection.
By analogy to classical cryptography, we develop a "quantum public key" based cryptographic scheme in which the two public and private keys consist in each of two entangled beams of squeezed light. An analog message is encrypted by modulating the phase of the beam sent in public. The knowledge of the degree of non classical correlation between the beam quadratures measured in private and in public allows only the receiver to decrypt the message. Finally, in a view towards absolute security, we formally prove that any external intervention of an eavesdropper makes him vulnerable to any subsequent detection.
Cryptographic protocols can be classified by the type of security against eavesdropping which they provide. There exist mathematically secure schemes whose security relies on mathematical proofs (like the Vernam cipher discussed below) or conjectures (like public key RSA encryption) about the complexity of deciphering the message without possessing the correct key. The majority of current secure public Internet connections rely on such schemes. Alternatively, a cryptographic setup may provide a physically secure method for communicating. In these setups the security is provided by the physical laws governing the communication protocol. Here we first discuss a provably secure classical communication protocol and then quantum methods for distributing the necessary keys. The BB84 protocol relies on the impossibility of perfectly distinguishing non-orthogonal quantum states from one copy of the quantum system. The scheme was invented in 1984 and is the first of its kind. In contrast, the Ekert91 protocol makes use of Bell correlations between entangled pairs of photons. These correlations are destroyed when Eve attempts to make a measurement on one of the particles but also when imperfections, such as decoherence processes, affect the scheme. As long as no such “elements of reality” are introduced, and Bell correlations violating local realism can be generated by Alice and Bob, no eavesdropper can be present. One-time pads and the Vernam cipher The Vernam cipher is a cryptographic protocol which allows the encryption and decryption protocol to be publicly known. The security of the protocol relies entirely on the key which is private and not publicly known. Alice and Bob share identical n -bit secret key strings (one-time pad).
Quantum cryptography with the predetermined key was experimentally realized using Einstein-Podolsky-Rosen(EPR) correlations of continuously bright optical beams. Only one of two EPR correlated beams is transmitted with the signals modulated on quadrature phases and amplitudes, and the other one is retained by the authorized receiver. The modulated small signals are totally submerged in the large quantum noise of the signal beam, therefore nobody except the authorized receiver can decode the signals. Usability of imperfect quantum correlation, high transmission and detection efficiencies, and security provided by quantum mechanics are the favorable features of the presented scheme.
In a previous paper certain measurable criteria have been derived, that are sufficient to demonstrate the existence of Einstein-Podolsky-Rosen (EPR) correlations for measurements with continuous variable outcomes. Here it is shown how such EPR criteria, which do not demand perfect EPR correlations, can be used to prove the extent of security for continuous variable quantum cryptographic schemes (in analogy to that proposed by Ekert) where Alice and Bob hope to construct a secure sequence of values from measurements performed on continuous-variable EPR-correlated fields sent from a distant source. It is proven that the demonstration of the EPR criterion on Alice's and Bob's joint statistics compels a necessary loss in the ability to infer the results shared by Alice and Bob, by measurements performed on any third channel potentially representing an eavesdropper (Eve). This result makes no assumption about the nature of the quantum source of the fields transmitted to Alice and Bob, except that the EPR correlations are observed at the final detector locations. In this way a means is provided to establish security in the presence of some loss and less than optimal correlation, and against any eavesdropping strategy employed by Eve prior to detection of the fields by Alice and Bob.
Scheme of quantum cryptography based on single mode quadrature phase and amplitude squeezed state lights is presented. The binary key is obtained by modulating the phase quadrature or amplitude quadrature of the quadrature squeezed coherent state. The uncertainty relation of quantum mechanics provides the quantum protection. Eavesdropping from optical tapping will degrade the signal to noise ratio of the results measured by the authorized receiver and hence be revealed. Comparing with that using a coherent state light, the application of the squeezed state light enhances the security significantly.