A secure communication game is considered for the cognitive channel with a confidential primary message, where the primary user is interested in maximizing its secure rate with lowest possible power consumption and the utility of the cognitive user is a weighted sum of the primary secrecy rate and the cognitive rate (corresponds to a spectrum law in favor of the legacy owners of the spectrum). An achievable rate region is derived for the channel with message splitting at the cognitive radio and noise forwarding. The game considers the case with no common message, but shows that even this limited scenario can still be beneficial. The established Nash Equilibrium (NE) shows that the cognitive user trades noise for bits. The results are also interesting in the sense that both users can benefit (by playing the distributed game) compared to their throughput resulting from the non-cooperative scenario.