Multi-receiver Authentication Scheme for Multiple Messages Based on Linear Codes

In this paper, we construct an authentication scheme for multi-receivers and multiple messages based on a linear code C. This construction can be regarded as a generalization of the authentication scheme given by Safavi-Naini and Wang [8]. Actually, we notice that the scheme of Safavi-Naini and Wang is constructed with Reed-Solomon codes. The generalization to linear codes has the similar advantages as generalizing Shamir’s secret sharing scheme to linear secret sharing sceme based on linear codes [1, 6, 5, 7, 9]. For a fixed message base field Fq, our scheme allows arbitrarily many receivers to check the integrity of their own messages, while the scheme of Safavi-Naini and Wang has a constraint on the number of verifying receivers V 6 q. And we introduce access structure in our scheme. Massey [5] characterized the access structure of linear secret sharing scheme by minimal codewords in the dual code whose first component is 1. We slightly modify the definition of minimal codewords in [5]. Let C be a [V, k] linear code. For any coordinate i ∈ {1, 2, · · · ,V}, a codeword ~c in C is called minimal respect to i if the codeword ~c has component 1 at the i-th coordinate and there is no other codeword whose i-th component is 1 with support strictly contained in that of ~c. Then the security of receiver Ri in our authentication scheme is characterized by the minimal codewords respect to i in the dual code C . Authentication scheme, linear codes, secret sharing, minimal codewords, substitution attack.