Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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. 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 $C^\bot$.

9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg