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A DC programming approach for solving a centralized group key management problem

Author

Listed:
  • Hoai An Le Thi

    (Université de Lorraine
    Institut Universitaire de France (IUF))

  • Thi Tuyet Trinh Nguyen

    (Université de Lorraine)

  • Hoang Phuc Hau Luu

    (Université de Lorraine)

Abstract

A single trusted entity known as a Key Server is in charge of key generation, distribution, and management in centralized key management schemes. To prevent eavesdropping and protect the exchange content, a group key is used to encrypt the group communication. This management mechanism is typically based on a binary tree structure. When the membership of a group changes dynamically, the group key must be changed, triggering a certain updated cost. This paper addresses an important problem in centralized dynamic group key management. It consists in finding a set of leaf nodes in a binary key tree to insert new members with minimal insertion cost and keeping the tree as balanced as possible. The two mentioned important objectives are combined into a unified (deterministic) optimization model whose objective function contains discontinuous step functions with binary variables, which is known to be NP-hard. We then reformulate the problem as a combinatorial optimization program with continuous objective by introducing new binary variables. Applying penalty techniques, it results in a standard DC (Difference of Convex functions) program that can be solved efficiently by DCA (DC algorithm). Besides, the insertion nodes must be the leaf nodes, we introduce a two-step algorithm to reduce the model complexity: the first is to find the set of leaf nodes, while the second is to solve the simplified optimization problem. Numerical experiments have been studied intensively to justify the merit of our proposed model as well as the corresponding DCA.

Suggested Citation

  • Hoai An Le Thi & Thi Tuyet Trinh Nguyen & Hoang Phuc Hau Luu, 2022. "A DC programming approach for solving a centralized group key management problem," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3165-3193, December.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:5:d:10.1007_s10878-022-00862-1
    DOI: 10.1007/s10878-022-00862-1
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    References listed on IDEAS

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    1. Tao Pham Dinh & Nam Nguyen Canh & Hoai Le Thi, 2010. "An efficient combined DCA and B&B using DC/SDP relaxation for globally solving binary quadratic programs," Journal of Global Optimization, Springer, vol. 48(4), pages 595-632, December.
    2. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
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