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DC programming and DCA for enhancing physical layer security via cooperative jamming. (English) Zbl 1391.90166

Summary: The explosive development of computational tools these days is threatening security of cryptographic algorithms, which are regarded as primary traditional methods for ensuring information security. The physical layer security approach is introduced as a method for both improving confidentiality of the secret key distribution in cryptography and enabling the data transmission without relaying on higher-layer encryption. In this paper, the cooperative jamming paradigm – one of the techniques used in the physical layer is studied and the resulting power allocation problem with the aim of maximizing the sum of secrecy rates subject to power constraints is formulated as a nonconvex optimization problem. The objective function is a so-called DC (difference of convex functions) function, and some constraints are coupling. We propose a new DC formulation and develop an efficient DCA (DC algorithm) to deal with this nonconvex program. The DCA introduces the elegant concept of approximating the original nonconvex program by a sequence of convex ones: at each iteration of DCA requires solution of a convex subproblem. The main advantage of the proposed approach is that it leads to strongly convex quadratic subproblems with separate variables in the objective function, which can be tackled by both distributed and centralized methods. One of the major contributions of the paper is to develop a highly efficient distributed algorithm to solve the convex subproblem. We adopt the dual decomposition method that results in computing iteratively the projection of points onto a very simple structural set which can be determined by an inexpensive procedure. The numerical results show the efficiency and the superiority of the new DCA based algorithm compared with existing approaches.

MSC:

90B18 Communication networks in operations research
90C26 Nonconvex programming, global optimization
90C56 Derivative-free methods and methods using generalized derivatives

Software:

PSwarm; CPLEX; MINOS
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Full Text: DOI

References:

[1] Kapoor, G.; Piramithu, S., Vulnerabilities in some recently proposed RFID ownership transfer protocols, IEEE Commun Lett, 14, 3, 260-262, (2010)
[2] Barenghi, A.; Breveglieri, L.; Koren, I.; Naccache, D., Fault injection attacks on cryptographic devices: theory, practice, and countermeasures, Proc IEEE, 100, 11, 3056-3076, (2012)
[3] Schneier, B., Cryptographic design vulnerabilities, IEEE Comput, 31, 9, 26-33, (1998)
[4] Goel, S.; Negi, R., Guaranteeing secrecy using artificial noise, IEEE Trans Wireless Commun, 7, 6, 2180-2189, (2008)
[5] Yang, J.; Kim, I.-M.; Kim, D. I., Optimal cooperative jamming for multiuser broadcast channel with multiple eavesdroppers, IEEE Trans Wireless Commun, 12, 6, 2840-2852, (2013)
[6] Tekin, E.; Yener, A., The general Gaussian multiple-access and two-way wiretap channels: achievable rates and cooperative jamming, IEEE Trans Inform Theory, 54, 6, 2735-2751, (2008) · Zbl 1329.94034
[7] Dong, L.; Han, Z.; Petropulu, A.; Poor, H., Improving wireless physical layer security via cooperating relays, IEEE Trans Signal Process, 58, 3, 1875-1888, (2010) · Zbl 1392.94184
[8] He, X.; Yener, A., Cooperative jamming: the tale of friendly interference for secrecy, 65-88, (2010), Springer US Boston, MA
[9] Li, J.; Petropulu, A.; Weber, S., On cooperative relaying schemes for wireless physical layer security, IEEE Trans Signal Process, 59, 10, 4985-4997, (2011) · Zbl 1393.94848
[10] Stanojev, I.; Yener, A., Improving secrecy rate via spectrum leasing for friendly jamming, IEEE Trans Inf Forensics Secur, 12, 1, 134-145, (2013)
[11] Wyner, A. D., The wire-TAP channel, Bell Sys Tech Journ, 54, 1355-1387, (1975) · Zbl 0316.94017
[12] Pham Dinh, T.; Le Thi, H. A., Convex analysis approach to DC programming: theory, algorithms and applications, Acta Mathematica Vietnamica, 22, 1, 289-357, (1997)
[13] Pham Dinh, T.; Le Thi, H. A., A D.C. optimization algorithm for solving the trust-region subproblem, SIAM J Optim, 8, 2, 476-505, (1998) · Zbl 0913.65054
[14] Le Thi, H. A.; Pham Dinh, T., The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems, Annals Oper Res, 133, 23-46, (2005) · Zbl 1116.90122
[15] Pham Dinh, T.; Le Thi, H. A., Recent advances in DC programming and DCA, Transactions on Computational Intelligence XIII, vol. 8342, 1-37, (2014), Springer Berlin Heidelberg Berlin, Heidelberg
[16] Le Thi H.A.. DC programming and DCA. http://www.litauniv-lorrainefr/ lethi/. · Zbl 1322.90072
[17] Alvarado, A.; Scutari, G.; Pang, J.-S., A new decomposition method for multiuser DC-programming and its application, IEEE Trans Signal Process, 62, 11, 2984-2998, (2014) · Zbl 1393.90091
[18] Murtagh, B. A.; Saunders, M. A., Minos 5.1 user’s guide, Tech. Rep. SOL 83-20R, (1983), Stanford Univ., CA, USA
[19] Vaz, A. I.F.; Vicente, L. N., A particle swarm pattern search method for bound constrained global optimization, J Global Optim, 39, 197-219, (2007) · Zbl 1180.90252
[20] Jorswieck, E.; Wolf, A.; Gerbracht, S., Secrecy on the physical layer in wireless networks, 20, 413-435, (2010), INTECH
[21] Wang, C.; Wang, H.-M.; Ng, D. W.K.; Xia, X.-G.; Liu, C., Joint beamforming and power allocation for secrecy in peer-to-peer relay networks, IEEE Trans Wireless Commun, 14, 6, 3280-3293, (2015)
[22] Zhou, J.; Cao, R.; Gao, H.; Zhang, C.; Lv, T., Secure beamforming design in wiretap MISO interference channels, Proceedings of the 2015 IEEE 81st vehicular technology conference (VTC Spring), 1-5, (2015)
[23] Vucic, N.; Schubert, M., DC programming approach for resource allocation in wireless networks, Proceedings of the 8th international symposium on modeling and optimization in mobile, Ad Hoc and wireless networks, 380-386, (2010)
[24] Kha, H. H.; Tuan, H. D.; Nguyen, H. H., Fast global optimal power allocation in wireless network by local DC programming, IEEE Trans On Wireless Commun, 11, 2, 510-512, (2012)
[25] Al-Shatri, A.; Weber, T., Achieving the maximum sum rate using DC programming in cellular networks, IEEE Trans Signal Process, 60, 3, 1331-1341, (2012) · Zbl 1393.94004
[26] Le Thi, H. A.; Nguyen, Q. T.; Phan, K. T.; Pham Dinh, T., DC programming and DCA based cross-layer optimization in multi-hop TDMA networks, Proceedings of the 5th asian conference intelligent information and database systems, ACIIDS 2013, Kuala Lumpur, Malaysia, March 18-20, 2013 Part II, 398-408, (2013), Springer Berlin Heidelberg Berlin, Heidelberg
[27] Le Thi, H. A.; Pham Dinh, T., Network utility maximisation: A DC programming approach for sigmoidal utility function, Proceedings of the 2013 international conference on advanced technologies for communications (ATC 2013), 50-54, (2013)
[28] Ta, A. S.; Le Thi, H. A.; Khadraoui, D.; Pham Dinh, T., Solving QoS routing problems by DCA, Proceedings of the second international conference on intelligent information and database systems, ACIIDS, Hue City, Vietnam, March 24-26, 2010. Part II, 460-470, (2010), Springer Berlin Heidelberg Berlin, Heidelberg
[29] Ta, A. S.; Le Thi, H. A.; Khadraoui, D.; Pham Dinh, T., Solving partitioning-hub location-routing problem using DCA, J Ind Manag Optim, 8, 1, 87-102, (2012) · Zbl 1364.90219
[30] Ta, A. S.; Pham Dinh, T.; Le Thi, H. A.; Khadraoui, D., Solving many to many multicast QoS routing problem using DCA and proximal decomposition technique, Proceedings of 2012 international conference on computing, networking and communications (ICNC), 809-814, (2012)
[31] Le Thi, H. A.; Pham Dinh, T., DC programming in communication systems: challenging problems and methods, Vietnam J Comput Sci, 1, 1, 15-28, (2014)
[32] Le Thi, H. A.; Vo, X. T.; Le, H. M.; Pham Dinh, T., DC approximation approaches for sparse optimization, Eur J Oper Res, 244, 1, 26-46, (2015) · Zbl 1346.90819
[33] Le Thi, H. A.; Vo, X. T.; Pham Dinh, T., Feature selection for linear SVMs under uncertain data: robust optimization based on difference of convex functions algorithms, Neural Netw, 59, 36-50, (2014) · Zbl 1327.90236
[34] Le Thi, H. A.; Nguyen, M. C.; Pham Dinh, T., A DC programming approach for finding communities in networks, Neural Comput, 26, 12, 2827-2854, (2014)
[35] Le Thi, H. A.; Nguyen, M. C.; Pham Dinh, T., Self-organizing maps by difference of convex functions optimization, Data Mining Knowl Discov, 28, 1336-1365, (2014) · Zbl 1342.90147
[36] IBM ILOG CPLEX Optimizer. http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/.
[37] Levitin, E. S.; Polyak, B. T., Constrained minimization methods, Comput Math Appl, 6, 5, 1-50, (1966)
[38] Jean-Baptiste Hiriart-Urruty, C. L., Convex analysis and minimization algorithms i: fundamentals, Grundlehren der mathematischen Wissenschaften 305, (1993), Springer-Verlag Berlin Heidelberg · Zbl 0795.49001
[39] Maculan, N.; Santiago, C. P.; Macambira, E. M.; Jardim, M. H.C., An O(n) algorithm for projecting a vector on the intersection of a hyperplane and a box in \(\mathbb{R}^n\), J Optim Theory Appl, 117, 3, 553-574, (2003) · Zbl 1115.90397
[40] Czyzyk, J.; Mesnier, M. P.; Moré, J. J., The NEOS server, IEEE J Comput Sci Eng, 5, 3, 68-75, (1998)
[41] Bertsekas, D. P.; Nedic, A.; Ozdaglar, E., Convex analysis and optimization, (2003), Athena Sicientific Belmont · Zbl 1140.90001
[42] Beck, A.; Nedic, A.; Ozdaglar, A.; Teboulle, M., An o(1/k) gradient method for network resource allocation problems, IEEE Trans Control Netw Syst, 1, 1, 64-73, (2014) · Zbl 1370.90290
[43] Rockafellar; Tyrrell, R.; Roger, J. B., Variational analysis, vol. 317, (1998), Spinger · Zbl 0888.49001
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