Multi-receiver Authentication Scheme for Multiple Messages Based on Linear Codes
This work provides a more flexible authentication scheme for secure communication systems, though it is incremental as it builds directly on prior methods.
The paper tackles the problem of authenticating messages for multiple receivers by generalizing an existing scheme from Reed-Solomon codes to linear codes, allowing arbitrarily many receivers to verify message integrity without the previous constraint of V ≤ q and incorporating access structures based on minimal codewords in the dual code.
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. 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. For a fixed message base field $\f$, 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 $V\leqslant q$. And we introduce access structure in our scheme. Massey 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 \cite{Massey93}. Let $C$ be a $[V,k]$ linear code. For any coordinate $i\in \{1,2,\cdots,V\}$, a codeword $\vec{c}$ in $C$ is called minimal respect to $i$ if the codeword $\vec{c}$ 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 $\vec{c}$. Then the security of receiver $R_i$ in our authentication scheme is characterized by the minimal codewords respect to $i$ in the dual code $C^\bot$.