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arXiv:0807.1937

Security of two-way quantum cryptography against asymmetric Gaussian attacks

Stefano Pirandola, Stefano Mancini, Seth Lloyd, Samuel L. Braunstein

Published Jul 11, 2008• 3 citations
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Abstract

Recently, we have shown the advantages of two-way quantum communications in continuous variable quantum cryptography. Thanks to this new approach, two honest users can achieve a non-trivial security enhancement as long as the Gaussian interactions of an eavesdropper are independent and identical. In this work, we consider asymmetric strategies where the Gaussian interactions can be different and classically correlated. For several attacks of this kind, we prove that the enhancement of security still holds when the two-way protocols are used in direct reconciliation.

DOI
10.48550/arxiv.0807.1937

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Recently, we have shown the advantages of two-way quantum communications in continuous variable quantum cryptography. Thanks to this new approach, two honest users can achieve a non-trivial security enhancement as long as the Gaussian interactions of an eavesdropper are independent and identical. In this work, we consider asymmetric strategies where the Gaussian interactions can be different and classically correlated. For several attacks of this kind, we prove that the enhancement of security still holds when the two-way protocols are used in direct reconciliation.
We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks.
We consider a two-way quantum cryptographic protocol with coherent states assuming direct reconciliation. A detailed security analysis is performed considering a two-mode coherent attack, which represents the residual eavesdropping once the parties have reduced the general attack by applying symmetric random permutations. In this context we provide a general analytical expression for the key rate, discussing the impact of the residual two-mode correlations on the security of the scheme. In particular, we identify the optimal eavesdropping against two-way quantum communication, which is given by a two-mode coherent attack with symmetric and separable correlations.
We investigate the asymptotic security of one-way continuous variable quantum key distribution against Gaussian two-mode coherent attacks. The one-way protocol is implemented by arranging the channel uses in two-mode blocks. By applying symmetric random permutations over these blocks, the security analysis is in fact reduced to study two-mode coherent attacks and, in particular, Gaussian ones, due to the extremality of Gaussian states. We explicitly show that the use of two-mode Gaussian correlations by an eavesdropper leads to asymptotic secret key rates which are strictly larger than the rate obtained under standard single-mode Gaussian attacks.
We investigate the security against collective attacks of a continuous variable quantum key distribution scheme in the asymptotic key limit for a realistic setting. The quantum channel connecting the two honest parties is assumed to be lossy and imposes Gaussian noise on the observed quadrature distributions. Secret key rates are given for direct and reverse reconciliation schemes including post-selection in the collective attack scenario. The effect of a nonideal error correction and two-way communication in the classical post-processing step is also taken into account.