Secure network coding and non-malleable codes: Protection against linear tampering

At ICS 2010, Dziembowski et al. introduced the notion of Non-Malleable Codes (NMC), adapting the cryptographic notion of non-malleability to the coding theory. Using NMC, if an attacker modifies a codeword, decoding this modified codeword will return either the original message or a completely unrelated value. The property of non-malleability depends on a family of modifications authorized to the attacker. In their paper, Dziem-bowski et al. propose a construction valid for the family of all bit-wise independent functions. At ITW 2011, Chabanne et al. proposed another construction for non-malleable codes w.r.t. bit-wise independent tampering functions by drawing a parallel between NMC and the Wire-Tap Channel II. In this paper, we show that the construction using Linear Coset Coding proposed by Chabanne et al. is non-malleable w.r.t. a larger class of functions, by considering linear tampering. Our results are derived from security results on Secure Network Coding using Linear Coset Coding, introduced by El Rouayheb and Soljanin at ISIT 2007.