Research PaperOpen Access

Optimization-Based Strategies for the Error Removal Method in the Ideal, Symmetric KLJN Secure Key Exchanger

E. Collado

Centro de Innovación y Transferencia Tecnológica, Universidad Tecnológica de Panamá, Aguadulce, Coclé, Panamá

E-mail Address: edwin.collado@utp.ac.pa

Search for more papers by this author

and

Y. Saez

http://orcid.org/0000-0003-0823-2490

Centro Regional de Azuero, Universidad Tecnológica de Panamá, La Villa de Los Santos, Los Santos, Panamá

E-mail Address: yessica.saez@utp.ac.pa

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0219477519500044Cited by:1 (Source: Crossref)

Abstract

The Kirchhoff’s-Law-Johnson-Noise (KLJN) secure key exchanger is a simple, low-cost scheme that provides symmetric encryption with unconditional security in electronic communication. The key bits are generated based on measurements of the mean-square value of the noise voltage and/or current of the channel between the two communicating parties. In this work, a combined current–voltage measurement mode scenario and an error removal method for the ideal, symmetric KLJN secure key exchanger that uses an identical pair of resistors at both ends of the communication line were considered, which improves the fidelity and reduces the bit error probability compared to the schemes when either voltage or current measurement are being used. It has been shown in previous works that the error probability of the original, symmetric KLJN secure key exchanger decays exponentially with parameters such as the time window for performing the key exchange and other relevant criteria used in the interpretation of the key bits. The objective of this work is to develop optimization strategies for the ideal, symmetric KLJN secure key exchanger in order to obtain optimal values of these parameters while ensuring that errors are kept within acceptable values. For those strategies, closed-form solutions to the optimal values were derived by solving the Karush–Kuhn–Tucker (KKT) conditions. Numerical results show that the proposed optimization techniques not only ensure that the bit probability error remains within the desired limit, but also provide more flexibility to define the thresholds values, reduce the bit exchange period needed to guarantee an acceptable bit error probability, weaken Eve’s statistics, and improve the system resource managing.

Communicated by Zoltan Gingl

Keywords:

Remember to check out the Most Cited Articles!
Be inspired by these NEW Mathematics books for inspirations & latest information in your research area!

References

1. L. B. Kish , Totally secure classical communication utilizing Johnson (-like) noise and Kirchhoff’s law, Phys. Lett. A 352 (3) (2006) 178–182. Web of Science, Google Scholar
2. L. B. Kish , Kish cypher, The Story of KLJN for Unconditional Security (World Scientific, 2017). Link, Google Scholar
3. Y. Liang, H. V. Poor and S. Shamai , Inf. Theor. Sec. Found. Trends Commun. Inf. Theory 5 (2008) 355–580. Google Scholar
4. R. Mingesz, Z. Gingl and L. B. Kish , Johnson (-like)-Noise-Kirchhoff-Loop based secure classical communicator characteristics, for ranges of two to two thousand kilometers, via model-line, Phys. Lett. A 372 (7) (2008) 978–984. Web of Science, Google Scholar
5. L. B. Kish and T. Horvath , Notes on recent approaches concerning the Kirchhoff-Law-Johnson-Noise-based secure key exchange, Phys. Lett. A 373 (32) (2009) 901–904. Web of Science, Google Scholar
6. L. B. Kish and C. G. Granqvist , On the security of the Kirchhoff-Law-Johnson-Noise (KLJN) communicator, Quantum Inf. Process. 13 (10) (2014) 2213–2219. Web of Science, Google Scholar
7. D. Abbott and G. Schmera , Secure communications using the KLJN scheme, Scholarpedia 8 (8) (2013) 31157. Google Scholar
8. L. B. Kish, D. Abbott and C. G. Granqvist , Critical analysis of the Bennett-Riedel attack on secure cryptographic key distributions via the Kirchhoff-Law-Johnson-noise scheme, PLoS ONE 8 (1) (2013) e81810. Web of Science, Google Scholar
9. L. B. Kish , Protection against the man in the middle attack for the Kirchhoff-Loop Johnson (-like)-noise cipher and expansion by voltage-based security, Fluct. Noise Lett. 6 (1) (2005) L57–L63. Link, Web of Science, Google Scholar
10. L. B. Kish , Enhanced secure key exchange systems based on the Johnson-Noise scheme, Metrol. Meas. Syst. 20 (2) (2013) 191–204. Web of Science, Google Scholar
11. L. B. Kish , Enhanced usage of keys obtained by physical, unconditionally secure distributions, Fluctuat. Noise Lett. 14 (2015) 1550007. Link, Web of Science, Google Scholar
12. T. Horvath, L. B. Kish and J. Scheuer , Effective privacy amplification for secure classical communications, Europhys. Lett. 94 (2) (2011) 28002. Google Scholar
13. E. Gonzalez, L. B. Kish and R. S. Balog , Information theoretically secure, enhanced Johnson noise based key distribution over the smart grid with switched filters, PLoS ONE 8 (2013) e70206. Web of Science, Google Scholar
14. Y. Saez, X. Cao, L. B. Kish and G. Pesti , Securing vehicle communication systems by the KLJN key exchange protocol, Fluct. Noise Lett. 13 (2014) 1450020. Link, Web of Science, Google Scholar
15. X. Cao, Y. Saez, L. B. Kish and G. Pesti , On KLJN-based secure key distribution in vehicular communication networks, Fluct. Noise Lett. 14 (2015) 1550008. Link, Web of Science, Google Scholar
16. L. B. Kish and R. Mingesz , Totally secure classical networks with multipoint telecloning (teleportation) of classical bits through loops with Johnson-like noise, Fluct. Noise Lett. 6 (2) (2006) C9–C21. Link, Web of Science, Google Scholar
17. L. B. Kish and O. Saidi , Unconditionally secure computers, algorithms and hardware, such as memories, processors, keyboards, flash and hard drives, Fluct. Noise Lett. 8 (2) (2008) L95–L98. Link, Web of Science, Google Scholar
18. G. Vadai, Z. Gingl and R. Mingesz , Generalized Kirchhoff-Law-Johnson-Noise (KLJN) secure key exchange system using arbitrary resistors, Sci. Rep. 5 (2015) 13653. Web of Science, Google Scholar
19. R. Mingesz, N. Bors, G. Vadai and Z. Gingl , Performance and security analysis of the generalized Kirchhoff-Law-Johnson-Noise key exchange protocol, Proc. of the 24th Int. Conf. Noise and Flucturations (ICNF) (IEEE, Vilnius, Lithuania, 2017), pp. 200–203. Google Scholar
20. G. Vadai, Z Gingl and R. Mingesz , Generalized attack protection in the Kirchhoff-Law-Johnson-Noise secure key exchanger, IEEE Access 4 (2016) 1141–1147. Web of Science, Google Scholar
21. L. B. Kish and C. G. Granqvist , Metrol. Meas. Syst. 23 (2016) 3–11. Web of Science, Google Scholar
22. F. Hao , Kish’ key scheme is insecure, Proc. IEEE Information Security 153 (2006) 141–142. Google Scholar
23. J. Scheuer and A. Yariv , A classical key-distribution system based on Johnson (like) noise–how secure, Phys. Lett. A 305 (3) (2006) 737–740. Web of Science, Google Scholar
24. C. H. Bennett and C. J. Riedel, On the security of the key distribution based on Johnson-Nyquist Noise, arXiv:1303.7435v1 (2013). Google Scholar
25. L. B. Kish, Z. Gingl, R. Mingesz, G. Vadai, J. Smulko and C. G. Granqvist , Analysis of an attenuator artifact by Gunn-Allison-Abbot against the Kirchhoff-law–Johnson-Noise (KLJN) secure key exchange system, Fluct. Noise Lett. 14 (5) (2015) 1550011. Link, Web of Science, Google Scholar
26. L. J. Gunn, A. Allison and D. Abbott , A directional wave measurement attack against the Kish key distribution system, Sci. Rep. 4 (2014) 6461. Web of Science, Google Scholar
27. L. J. Gunn, A. Allison and D. Abbott , A new transient attack on the Kish key distribution system, IEEE Access 3 (2015) 1640–1648. Web of Science, Google Scholar
28. H. P. Chen, M. Mohammad and L. B. Kish , Current injection attack against the KLJN secure key exchange, Metrol. Meas. Syst. 23 (2) (2016) 173–181. Web of Science, Google Scholar
29. L. B. Kish , Response to Feng Hao’s paper ‘Kish’s key exchange schemis insecure, Fluct. Noise Lett. 6 (4) (2006) C37–C41. Link, Web of Science, Google Scholar
30. L. B. Kish , Response to Scheuer–Yariv: ‘A classical key-distribution system based on Johnson (like) noise—How secure?’ Phys. Lett. A 359 (6) (2006) 741–744. Web of Science, Google Scholar
31. H.-P. Chen, L. B. Kish, C.-G. Granqvist and G. Schmera , On the ‘cracking’ scheme in the paper ‘a directional coupler attack against the Kish key distribution system’ by Gunn, Allison and Abbott, Metrol. Meas. Syst. 21 (3) (2014) 389–400. Web of Science, Google Scholar
32. L. B. Kish and C.-G. Granqvist , Elimination of a second-law-attack, and all cable-resistance-based attacks, in the Kirchhoff-law-Johnson noise (KLJN) secure key exchange system, Entropy 16 (10) (2014) 5223–5231. Web of Science, Google Scholar
33. L. B. Kish and J. Scheuer , Noise in the wire: The real impact of wire resistance for the Johnson (-like) noise based secure communicator, Phys. Lett. A 374 (2010) 2140–2142. Web of Science, Google Scholar
34. R. Mingesz, L. B. Kish, Z. Gingl, C. G. Granqvist, H. Wen, F. Peper, T. Eubanks and G. Schmera , Unconditional security by the laws of classical physics, Metrol. Meas. Syst. 20 (1) (2013) 3–16. Web of Science, Google Scholar
35. Y. Saez and L. B. Kish , Errors and their mitigation at the Kirchhoff-Law-Johnson-noise secure key exchange, PLoS ONE 8 (11) (2013) e81103. Web of Science, Google Scholar
36. Y. Saez, L. B. Kish, R. Mingesz, Z. Gingl and C. G. Granqvist , Current and voltage based bit errors and their combined mitigation for the Kirchhoff-Law–Johnson-noise secure key exchange, J. Comput. Electron. 13 (1) (2014) 271–277. Web of Science, Google Scholar
37. Y. Saez, L. B. Kish, R. Mingesz, Z. Gingl and C. G. Granqvist , Bit errors in the Kirchhoff-Law-Johnson-noise secure key exchange, Int. J. Mod. Phys. Conf. Series 33 (2014) 1460367. Link, Google Scholar
38. E. Collado and Y. Saez , Optimization applied to the KLJN secure key exchange system with maximum fixed error guarantee, Revista I+D tecnológico 13 (2) (2017) 100–110. Google Scholar
39. L. B. Kish, R. Mingesz, Z. Gingl and C. G. Granqvist , Spectra for the Product of Gaussian Noises, Metrol. Meas. Syst. 19 (4) (2012) 653–658. Web of Science, Google Scholar
40. S. O. Rice , Mathematical analysis of random noise, Bell Labs Tech. J. 23 (3) (1944) 282–332. Google Scholar
41. I. Rychlik , On some reliability applications of Rice’s formula for the intensity of level crossing, Extremes 3 (4) (2000) 331–348. Google Scholar
42. L. B. Kish , End of Moore’s Law; thermal (Noise) death of integration in micro and nano electronics, Phys. Lett. A 305 (3) (2002) 144–149. Web of Science, Google Scholar
43. L. B. Kish and C. G. Granqvist , Electrical Maxwell demon and szilard engine utilizing Johnson noise, measurement, logic and control, PLoS ONE 7 (2012) e46800. Web of Science, Google Scholar
44. S. Boyd and L. Vandenberghe , Convex Optimization (Cambridge University Press, Cambridge, UK, 2004). Google Scholar

Vol. 18, No. 01

Metrics

Downloaded 224 times

History

Received 30 May 2018

Accepted 3 October 2018

Published: 23 October 2018

Information

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.

Keywords

PDF download

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Optimization-Based Strategies for the Error Removal Method in the Ideal, Symmetric KLJN Secure Key Exchanger

Abstract

Recommended