Оптимальні LDPC матриці для виявлення помилок в квантових бітах у системах QKD

Bohdan Olehovych Bilash

doi:10.20535/2523-4455.mea.201253

Vol. 25 · Issue 1 · 2020 Jul 6, 2020 Electronic Systems and Signals

Optimal Low Density Parity Check Matrices to Correct Quantum Key Errors for QKD

Bohdan Olehovych Bilash Corresponding Національний технічний університет України "Київський політехнічний інститут імені Ігоря Сікорського" Ukraine

Pages27-32 PublishedJul 6, 2020

PDF (Ukrainian)

VOL 25 · ISS 1 · 2020 View issue

Abstract

In this paper, the parity-check matrices that can be used in low density parity check (LDPC) based error correction method for quantum key distribution are analyzed. The quantum key distribution system has inevitable errors in sifted key that must be corrected by an error correction algorithm to create a secure key. In this analysis, 1000-bit sifted keys are divided into 50 parts. The algorithm creates 50 syndromes corresponding to each part by multiplying 10 × 20 bit parity-check matrices. The algorithm sends the generated syndrome to the other side, which also divides the sifted key into 50 parts, creates a syndrome from each part, and compares with the received syndrome. If the syndromes are different, these sifted key parts are discarded. However, there may be situations where different parts may have the same syndromes. Therefore, it is necessary to find such an optimal matrix that removes the probability of getting the same syndromes at different parts of the sifted key.

Keywords

#QKD #LDPC #error correction #parity-check matrix #post-processing

References

S. Wiesner, “Conjugate coding,” ACM SIGACT News, vol. 15, no. 1, pp. 78–88, Jan. 1983, DOI:10.1145/1008908.1008920.
R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM, vol. 21, no. 2, pp. 120–126, Feb. 1978, DOI: 10.1145/359340.359342.
C. H. Bennett and G. Brassard, “BB84highest.pdf,” Proceedings of IEEE International Conference on Computers, Systems and Signal Processing. pp. 174–179, 1984.
P. Sibson et al., “Chip-based quantum key distribution,” Nat. Commun., vol. 8, no. May 2016, 2017, DOI: 10.1038/ncomms13984.
M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate–distance limit of quantum key distribution without quantum repeaters,” Nature, vol. 557, no. 7705, pp. 400–403, May 2018, DOI: 10.1038/s41586-018-0066-6.
Z. Yuan et al., “10-Mb/s Quantum Key Distribution,” J. Light. Technol., vol. 36, no. 16, pp. 3427–3433, 2018, DOI: 10.1109/JLT.2018.2843136.
H.-K. Lo, M. Curty, and B. Qi, “Measurement-Device-Independent Quantum Key Distribution,” Phys. Rev. Lett., vol. 108, no. 13, p. 130503, Mar. 2012, DOI: 10.1103/PhysRevLett.108.130503.
C. H. Park et al., “Practical plug-and-play measurement-device-independent quantum key distribution with polarization division multiplexing,” IEEE Access, vol. 6, pp. 58587–58593, 2018, DOI: 10.1109/ACCESS.2018.2874028.
B. K. Park, M. K. Woo, Y.-S. Kim, Y.-W. Cho, S. Moon, and S.-W. Han, “User-independent optical path length compensation scheme with sub-nanosecond timing resolution for a 1 × N quantum key distribution network system,” Photonics Res., vol. 8, no. 3, p. 296, Mar. 2020, DOI: 10.1364/PRJ.377101.
T. A. Eriksson et al., “Crosstalk Impact on Continuous Variable Quantum Key Distribution in Multicore Fiber Transmission,” IEEE Photonics Technol. Lett., vol. 31, no. 6, pp. 467–470, 2019, DOI: 10.1109/LPT.2019.2898458.
G. Brassard and L. Salvail, “Secret-key reconciliation by public discussion,” Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), vol. 765 LNCS, pp. 410–423, 1994, DOI: 10.1007/3-540-48285-7_35.
W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. H. Nickel, C. H. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A - At. Mol. Opt. Phys., vol. 67, no. 5, p. 8, 2003, DOI: 10.1103/PhysRevA.67.052303.
Gallager, “Low density parity check codes,” 1963.
D. J. C. Mackay and R. M. Neal, “Good codes based on very sparse matrices,” in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 1995, vol. 1025, pp. 100–111, DOI: 10.1007/3-540-60693-9_13.
D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 399–431, 1999, DOI: 10.1109/18.748992.
N. Walenta et al., “A fast and versatile quantum key distribution system with hardware key distillation and wavelength multiplexing,” New J. Phys., vol. 16, 2014, DOI: 10.1088/1367-2630/16/1/013047.
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes. Cambridge University Press, 2003.
Radford M. Neal, “Software for Low Density Parity Check Codes.” 2012.

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[1] S. Wiesner, “Conjugate coding,” ACM SIGACT News, vol. 15, no. 1, pp. 78–88, Jan. 1983, DOI:10.1145/1008908.1008920.

[2] R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM, vol. 21, no. 2, pp. 120–126, Feb. 1978, DOI: 10.1145/359340.359342.

[3] C. H. Bennett and G. Brassard, “BB84highest.pdf,” Proceedings of IEEE International Conference on Computers, Systems and Signal Processing. pp. 174–179, 1984.

[4] P. Sibson et al., “Chip-based quantum key distribution,” Nat. Commun., vol. 8, no. May 2016, 2017, DOI: 10.1038/ncomms13984.

[5] M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate–distance limit of quantum key distribution without quantum repeaters,” Nature, vol. 557, no. 7705, pp. 400–403, May 2018, DOI: 10.1038/s41586-018-0066-6.

[6] Z. Yuan et al., “10-Mb/s Quantum Key Distribution,” J. Light. Technol., vol. 36, no. 16, pp. 3427–3433, 2018, DOI: 10.1109/JLT.2018.2843136.

[7] H.-K. Lo, M. Curty, and B. Qi, “Measurement-Device-Independent Quantum Key Distribution,” Phys. Rev. Lett., vol. 108, no. 13, p. 130503, Mar. 2012, DOI: 10.1103/PhysRevLett.108.130503.

[8] C. H. Park et al., “Practical plug-and-play measurement-device-independent quantum key distribution with polarization division multiplexing,” IEEE Access, vol. 6, pp. 58587–58593, 2018, DOI: 10.1109/ACCESS.2018.2874028.

[9] B. K. Park, M. K. Woo, Y.-S. Kim, Y.-W. Cho, S. Moon, and S.-W. Han, “User-independent optical path length compensation scheme with sub-nanosecond timing resolution for a 1 × N quantum key distribution network system,” Photonics Res., vol. 8, no. 3, p. 296, Mar. 2020, DOI: 10.1364/PRJ.377101.

[10] T. A. Eriksson et al., “Crosstalk Impact on Continuous Variable Quantum Key Distribution in Multicore Fiber Transmission,” IEEE Photonics Technol. Lett., vol. 31, no. 6, pp. 467–470, 2019, DOI: 10.1109/LPT.2019.2898458.

[11] G. Brassard and L. Salvail, “Secret-key reconciliation by public discussion,” Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), vol. 765 LNCS, pp. 410–423, 1994, DOI: 10.1007/3-540-48285-7_35.

[12] W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. H. Nickel, C. H. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A - At. Mol. Opt. Phys., vol. 67, no. 5, p. 8, 2003, DOI: 10.1103/PhysRevA.67.052303.

[13] Gallager, “Low density parity check codes,” 1963.

[14] D. J. C. Mackay and R. M. Neal, “Good codes based on very sparse matrices,” in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 1995, vol. 1025, pp. 100–111, DOI: 10.1007/3-540-60693-9_13.

[15] D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 399–431, 1999, DOI: 10.1109/18.748992.

[16] N. Walenta et al., “A fast and versatile quantum key distribution system with hardware key distillation and wavelength multiplexing,” New J. Phys., vol. 16, 2014, DOI: 10.1088/1367-2630/16/1/013047.

[17] W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes. Cambridge University Press, 2003.

[18] Radford M. Neal, “Software for Low Density Parity Check Codes.” 2012.

Optimal Low Density Parity Check Matrices to Correct Quantum Key Errors for QKD

Abstract

Keywords

References

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