A TWOOA Construction for Multi-Receiver Multi-Message Authentication Codes

A (k, n; w) multi-receiver multi-message authentication code allows a transmitter to broadcast up to w − 1 different authenticated messages to n receivers in such a way that (1) not only an opponent but also any up to k − 1 receivers cannot cheat any other receivers, and (2) all the receivers can independently verify the authenticity of the messages. Obana and Kurosawa (Designs, Codes and Cryptography 22 (2001), 47-63) used a special pair of orthogonal arrays, called TWOOA, to construct a (k, n; 2) multi-receiver single-message authentication code. In this paper, we generalize the notion of a TWOOA, and then use this generalized TWOOA to construct a (k, n; w) multi-receiver multi-message authentication code, which exceeds that of Savavi-Naini and Wang (Proc. of Eurocrypt’98, LNCS 1403, Springera (1998), 527-541) at least in the numbers of receivers and authenticated messages. The structures of TWOOAs are investigated. Two constructions for TWOOAs are also provided. ∗ Corresponding author