Secure Computation-and-Forward With Linear Codes

We discuss secure transmission via an untrusted relay when we have a multiple access phase from two nodes to the relay and a broadcast phase from the relay to the two nodes. To realize the security, we construct a code that securely transmits the modulo sum of the messages of two nodes via a multiple access channel. In this code, the relay cannot obtain any information with respect to the message of each node, and can decode only the modulo-sum of the messages of the two nodes. Our code is constructed by simple combination of an existing linear code and universal2 hash function.