Universal Strongly Secure Network Coding with Dependent and Non-Uniform Messages

We construct a secure network coding that is strongly secure in the sense of Harada and Yamamoto [19] and universal secure in the sense of Silva and Kschischang [28], [29], while allowing arbitrary small but nonzero mutual information to the eavesdropper. Our secure network coding allows statistically dependent and non-uniform multiple secret messages, while all previous constructions of weakly or strongly secure network coding assumed independent and uniform messages, which is difficult to be ensured in practice.