The Capacity of a Channel with a One-Way Function

Subliminal channels can hide the existence of secret messages, and then they are divided into broadband ones and narrowband ones. While a large amount of information can be transmitted over a broadband one, only a small amount can be done over a narrowband one. It is easy to show that a channel can only be a narrowband one, when a one-way function whose image size is su ciently large and which has no trapdoor is in between a carrier state which a receiver can observe and a parameter which the transmitter can control. However it is not clear that how much capacity the communication channel has and how many bits can be transmitted with how much error rate. In this paper, we clarify that, and also consider methods to try to maximize the information bits being transmitted when the error rate is kept under a certain value.