Watermarking Identification Codes with Related Topics on Common Randomness

Watermarking identification codes were introduced by Y. Steinberg and N. Merhav. In this paper we assume that the attacker chooses an unknown (for both information hider and decoder) channel from a set of channels or a compound channel, to attack the watermark. We present two models. In the first model according to the output sequence of covertext the information hider generates side information componentwise as the secret key. In the second model the only constraint to the key space is an upper bound for its rate. We present lower bounds for the identification capacities in the above models, which include the Steinberg and Merhav results on lower bounds. For the models with a single channel, we obtain the capacities of common randomness. For the models with a compound channel, we have lower and upper bounds and the differences of lower and upper bounds are due to the exchange and different orders of the max-min operations.