Reduction Theorem for Secrecy over Linear Network Code for Active Attacks

Masahito Hayashi; Masaki Owari; Go Kato; Ning Cai

doi:10.3390/e22091053

Reduction Theorem for Secrecy over Linear Network Code for Active Attacks

Entropy (Basel). 2020 Sep 21;22(9):1053. doi: 10.3390/e22091053.

Authors

Masahito Hayashi^{1

2

3

4}, Masaki Owari⁵, Go Kato⁶, Ning Cai⁷

Affiliations

¹ Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
² Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
³ Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
⁴ Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan.
⁵ Department of Computer Science, Faculty of Informatics, Shizuoka University, Shizuoka 422-8529, Japan.
⁶ NTT Communication Science Laboratories, NTT Corporation, Tokyo 100-8116, Japan.
⁷ The School of Information Science and Technology, ShanghaiTech University, Middle Huaxia Road no. 393, Pudong, Shanghai 201210, China.

Abstract

We discuss the effect of sequential error injection on information leakage under a network code. We formulate a network code for the single transmission setting and the multiple transmission setting. Under this formulation, we show that the eavesdropper cannot increase the power of eavesdropping by sequential error injection when the operations in the network are linear operations. We demonstrated the usefulness of this reduction theorem by applying a concrete example of network.

Keywords: active attack; passive attack; secrecy analysis; secure network coding; sequential injection.

Abstract

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