Secure network and index coding equivalence: the last piece of the puzzle

An equivalence was shown between network coding and index coding. The equivalence allows for a network code for any given network-coding instance to be translated to an index code for a suitably constructed index-coding instance, and vice versa. The equivalence also holds for the opposite direction. A secure version of the equivalence in the presence of eavesdroppers was proven for the case where there is no decoding error and no information leakage to the eavesdroppers. For the case of non-zero decoding error and non-zero leakage, three out of the four directions required for an equivalence were proven. This paper proves the last direction, thereby completing the equivalence between secure network coding and secure index coding.