Geodesic
Quantum Stream Ciphers: Impossibility of Unconditionally Strong Algorithms
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum probability, Tome 151 (2018), pp. 91-104.

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Stream ciphers is one of two large classes of ciphers with private keys in classical cryptography. In this paper, we introduce the concept of a quantum stream cipher. Special types of quantum stream ciphers were proposed earlier by numerous researchers. We prove a general result on the nonexistence of an absolutely strong quantum stream cipher if the length of the message is much longer than the length of the key. We analyze individual and collective attacks against the quantum stream cipher. A relationship between the problem of guessing the key by the opponent and the problem of distinguishing of random quantum states is established.
Keywords: quantum cryptography, stream ciphers, unconditionally strong algorithm, distinguishing of quantum states. 
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     title = {Quantum {Stream} {Ciphers:} {Impossibility} of {Unconditionally} {Strong} {Algorithms}},
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P. A. Tregubov; A. S. Trushechkin. Quantum Stream Ciphers: Impossibility of Unconditionally Strong Algorithms. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum probability, Tome 151 (2018), pp. 91-104. http://geodesic.mathdoc.fr/item/INTO_2018_151_a8/

[1] Alferov A. P., Zubov A. Yu., Kuzmin A. S., Cheremushkin A. V., Osnovy kriptografii, Gelios ARF, M., 2002

[2] Balygin K. A. i dr., “Prakticheskaya kvantovaya kriptografiya”, Pisma v ZhETF, 105:9 (2017), 570–576

[3] Kiktenko E. O. i dr., “Demonstratsiya seti kvantovogo raspredeleniya klyucha v gorodskikh optovolokonnykh liniyakh svyazi”, Kvant. elektr., 47:9 (2017), 798–802

[4] Marchenko V. A., Pastur L. A., “Raspredelenie sobstvennykh znachenii v nekotorykh ansamblyakh sluchainykh matrits”, Mat. sb., 72 (114):4 (1966), 507–536

[5] Nilsen M., Chang I., Kvantovye vychisleniya i kvantovaya informatsiya, Mir, M., 2006

[6] Kholevo A. S., Kvantovye sistemy, kanaly, informatsiya, MTsNMO, M., 2010

[7] Shennon K., “Teoriya svyazi v sekretnykh sistemakh”, Klod Shennon. Raboty po teorii informatsii i kibernetike, IL, M., 1963, 333–369

[8] Shnaier B., Prikladnaya kriptografiya, TRIUMF, M., 2003

[9] Bennett C. H., Brassard G., “Quantum cryptography: public keydistribution and coin tossing”, Proc. IEEE Int. Conf. on Comput. Syst. Signal Process., 1984, 175–179

[10] Chen T.-Y. et al., “Metropolitan all-pass and inter-city quantum communication network”, Opt. Express., 17:26 (2009), 27217–27225 | DOI

[11] Elliott C. et al., “Current status of the DARPA quantum network”, Proc. SPIE., 5815 (2005), 138–149 | DOI

[12] Gisin N., Ribordy G., Tittel W., Zbinden H., “Quantum cryptography”, Rev. Mod. Phys., 74:1 (2002), 145–195 | DOI

[13] Hirota O., Kurosawa K., “Immunity against correlation attack on quantum stream cipher by Yuen 2000 protocol”, Quant. Inform. Process., 6:2 (2007), 81–91 | DOI | MR | Zbl

[14] Kato K., “Quantum enigma cipher as a generalization of the quantum stream cipher”, Proc. SPIE., 9980 (2016), 998005 | DOI

[15] “Central limit theorem for linear eigenvalue statistics for a tensor product version of sample covariance matrices”, J. Theor. Probab., 31 (2018), Lytova A. | MR

[16] Montanaro A., “On the distinguishability of random quantum states”, Commun. Math. Phys., 273:3 (2007), 619–636 | DOI | MR | Zbl

[17] Peev M. et al., “The SECOQC quantum key distribution network in Vienna”, New J. Phys., 11 (2009), 075001 | DOI

[18] Price A. B., Rarity J. G., Erven C., A quantum key distribution protocol for rapid denial of service detection, arXiv: 1707.03331 [quant-ph]

[19] Qiu D., Li L., “Minimum-error discrimination of quantum states:New bounds and comparison”, Phys. Rev. A., 81:4 (2010), 042329 | DOI

[20] Sasaki M. et. al., “Field test of quantum key distribution in the Tokyo QKD Network”, Opt. Express., 19:11 (2011), 10387–10409 | DOI

[21] Shor P. W., “Algorithms for quantum computation: discrete logarithmsand factoring”, Found. Comput. Sci. Conf. Publ., 1994, 124–134 | MR

[22] Stucki D. et al. Long-term performance of the SwissQuantum quantum key distribution network in a field environment, New J. Phys., 13 (2011), 123001 | DOI

[23] Trushechkin A. S., Tregubov P. A., Kiktenko E. O., Kurochkin Y. V., Fedorov A. K., Quantum key distribution protocol with pseudorandom bases, arXiv: 1706.00611 [quant-ph]

[24] Yuen H., KCQ: A new approach to quantum cryptography, I. General principles and key generation, arXiv: quant-ph/0311061