Mathematical simulation of quantum protocol BB84 key distribution

The objective of this research is a mathematical simulation of quantum protocol bb84 key distribution in the MATLAB environment and evaluation of the cryptographic robustness of the transmitted data and its resistance to the attacks of the exhaustive values enumeration (such as the brute-force attack). Message passing through the quantum communication channel is carried out by means of generating random bit vectors, which demonstrate the choice of the polarization and measurement bases as well as the key agreement process through the conventional communication channel. Obtained during the mathematical simulation, the number of possible values subjected to the exhaustive enumeration, is immensely large, and the time for the enumeration of such values turned out to be more than the term of relevancy and importance of the intercepted information. The purpose of this work is to investigate the cryptographic robustness of quantum protocol bb84 key distribution and its resistance to the attacks such as the brute-force.

References

[1] Avdoshin S. Diskretnaya matematika. Modulyarnaya algebra, kriptografiya, kodirovanie [Discrete math. Modular algebra, cryptography, encoding]. Moscow, SINTEG publ., 2016, 260 p.

[2] Adamenko M. Osnovy klassicheskoy kriptologii. Sekrety shifrov i kodov [Fundamentals of classic cryptology. Secrets of ciphers and codes]. Moscow, Mashinostroenie publ., 2014, 256 p.

[3] Assange J. Cypherpunks: freedom and the future of the Internet. OR Books, 2016, 196 p. (Russ. ed.: Shifropanki: svoboda i budushchee Interneta. Moscow, Azbuka-Attikus publ., 2014, 574 p.)

[4] Kholevo A.S. Kvantovye sistemy, kanaly, informatsiya [Quantum systems, channels, information]. Moscow, MTsNMO publ., 2010, 328 p.

[5] Alferov A.P., Zubov A.Yu., Kuz’min A.S., Cheremushkin A.V. Osnovy kriptografii [Fundamentals of cryptography]. Moscow, Gelios ARV publ., 2002, 480 p.

[6] Schneier B. Applied cryptography: protocols, algorithms, and source code in C. Wiley, 1994, 618 p. (Russ. ed.: Prikladnaya kriptografiya. Moscow, Triumf publ., 2002, 816 p.)

[7] Bennett C.H., Brassard G. Quantum cryptography: public key distribution and coin tossing. Proc. IEEE Int. Conf. on Computers, Systems and Signal Processing, 1984, vol. 175, p. 8.

[8] Bennett C.H. Quantum cryptography using any two nonorthogonal states. Physical Review Letters, 1992, vol. 68, no. 21, pp. 3121–3124.

[9] Bennett C.H., Bessette F., Brassard G., et al. Experimental quantum cryptography. Journal of Cryptology, 1992, vol. 5, no. 1, pp. 3–28.

[10] Brassard G., Lutkenhaus N., Mor T., Sanders B.C. Limitations on practical quantum cryptography. Physical Review Letters, 2000, vol. 85, no. 6, pp. 1130–1133.

[11] Molotkov S.N. On a collective attack on the key in quantum cryptography on two nonorthogonal states. Pis’ma v ZhETF, 2004, vol. 80, no. 8, pp. 639–644. (Eng. version: Journal of Experimental and Theoretical Physics Letters, 2004, vol. 80, no. 8, pp. 563–567).

[12] Molotkov S.N. On the ultimate capabilities of the quantum key distribution with the control over the statistics of a non-single-photon source. Pis’ma v ZhETF, 2008, vol. 87, no. 10, pp. 674–679. (Eng. version: Journal of Experimental and Theoretical Physics Letters, 2008, vol. 87, no. 10, pp. 586–591.)

[13] Molotkov S.N. Quantum key distribution with the deterministic preparation and detection of quantum states. Pis’ma v ZhETF, 2010, vol. 91, no. 1, pp. 51–57. (Eng. version: Journal of Experimental and Theoretical Physics Letters, 2010, 91:1, 48–53.)

[14] Fedorov A.K. Sovremennoe sostoyanie kvantovoy kriptografii [Contemporary state of quantum cryptography]. Studencheskiy nauchnyy vestnik. Sb. tezisov obshcheuniversitetskoy nauch.-tekh. konf. «Studencheskaya nauchnaya vesna - 2011». T. X [Students science bulletin. Proc. Universiry Sci.-Tech. Conf “Students scientific spring-2011”. Vol. X]. Moscow, Bauman Press, 2012, pp. 81–83.

[15] Fedorov A.K. Protivodeystvie atake “Photon number splitting attack” pri kvantovom raspredelenii klyucha BB84 [“Photon number splitting attack” resistance at quantum distribution of BB84 key]. Studencheskiy nauchnyy vestnik. Sb. tezisov obshcheuniversitetskoy nauch.-tekh. konf. «Studencheskaya nauchnaya vesna — 2011». T. XI, ch. II [Students science bulletin. Proc. Universiry Sci.-Tech. Conf “Students scientific spring-2011”. Vol. XI. P. II]. Moscow, Bauman Press, 2012, pp. 204–205.