Complexity In Information Theoretic Security

Information theoretic security study is based on minimal or no information leaked to malicious users. Secure network coding scheme could be simple but the study and optimality of the secure network coding is analysis is complex task. Complexity is due to the randomness and distribution of the source symbol though random key distribution can be modeled as per simplified coding scheme.

Secure Network Coding scheme not only promise to secure transmission but also challenge keep optimal information rate. Security level increases with the increasing random key field size and conversely information rate reduces. Hence optimality of secure network coding is realized very important study in Secure Network Coding theory. 

Secure Linear Network Code

According to secure network coding theory and information theoretic security to the network code, a linear network code with word length of (j+r), j-dimensional message and r-dimensional random key to be secured linearly, illegitimate users will obtain message of length lesser than j+r that is less information than a source message symbol can deliver to legitimate users.

For above network code, each network channel is to of unit capacity and the network code is linear. If a malicious user has access to r-channels then network code is r-secure network code. A network code is w-imperfectly secure if there r<w<j+r channels are accessible to malicious users. A network code is weakly secure if there is no randomness introduced to message and the malicious users get strictly less amount of message than j and the corresponding network code is efficient codes with optimal information rate. 

For linear and unit capacity network channels, entropy of a coded symbol is equivalent to j+r and that eavesdropped by malicious user is with w-channel tapped is equivalently to w, where w is in between r and j+r.