Abstract
Network coding has emerged as a promising approach for peer-to-peer converged ubiquitous networks to increase network capacity and solve the block reconciliation problem. However, peer-to-peer systems with network coding suffer a severe security threat, known as pollution attack, in which malicious peers inject corrupted packets into the information flow. Previous solutions are either computationally expensive or too ineffective to limit pollution attacks with arbitrary collusion among malicious peers. In this paper, we propose time keys, an efficient security scheme which allows participating peers to efficiently detect corrupted packets by using time and space properties of network coding. Our work is an innovative security solution to frustrate pollution attacks with collusion based on time and space properties of network coding. In addition, time keys scheme provides an efficient packet verification without requiring the existence of any extra secure channels. We also present security analysis and simulations of our scheme, and results demonstrate the practicality and efficiency of time keys scheme.
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Acknowledgments
This work is supported by The National Basic Research Program of China (973 Program) (2012CB315900); The National High Technology Research and Development Program of China (863 Program) (2011AA01A103); Hunan Provincial Natural Science Foundation of China (11JJ7003); Natural Science Foundation of China (61070201); Program for Changjiang Scholars and Innovative Research Team in University (IRT1012).
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Appendix
Appendix
Theorem 1
The dimension of orthogonal space of Π X is equal to m.
Proof
Considering the rank-nullity theorem [9], we have r a n k(A) + n u l l i t y(A) = n for any m × n matrix A, where the dimension of the orthogonal space of A is called the nullity of A.
X is a n × (m + n) matrix whose ith row is x i , and r a n k(X) = n. Applying the rank-nullity theorem to our network coding system, we have:
So, dimension of orthogonal space of π X is equal to m. Theorem 1 has been proved. □
Theorem 2
Packets verification with pure orthogonality principle is not secure in pollution attacks with collusion.
Proof
If the orthogonality principle is satisfied, it does not imply that the received vector belongs to π X . If the malicious node knows the value of orthogonal vectors collected by its neighbor, it can easily find a corrupted vector that satisfies the orthogonality principle. During pollution attacks with collusion, malicious nodes can obtain most of orthogonal vectors, and they can easily destroy the packets verification and launch pollution attacks. Theorem 2 has been proved. □
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He, M., Gong, Z., Chen, L. et al. Securing network coding against pollution attacks in P2P converged ubiquitous networks. Peer-to-Peer Netw. Appl. 8, 642–650 (2015). https://doi.org/10.1007/s12083-013-0216-4
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DOI: https://doi.org/10.1007/s12083-013-0216-4