Construction of an Optimal (k,n) Multi‐Receiver Authentication Code Based on Orthogonal Arrays

ABSTRACT A multi‐receiver authentication code refers to a sender transmitting a message that needs to be authenticated to receivers, so that each receiver can verify it, and any receivers cannot deceive other receivers. In this paper, an optimal multi‐receiver authentication code is designed by constructing two orthogonal arrays, which satisfy that each column of one orthogonal array is friendly to the other orthogonal array. One orthogonal array with strength 2 is presented according to the mutually orthogonal Latin squares, and the other orthogonal array with strength is obtained by using Bush's construction. It is proved that the orthogonal array with strength is friendly to each column of the orthogonal array with strength 2. The probability of successful impersonation and substitution attacks from an opponent, and the number of encoding rules are calculated to verify that the constructed multi‐receiver authentication code is optimal.