Watermarking Identification Codes with Related Topics on Common Randomness

Abstract

Watermarking identification codes were introduced by Y. Steinberg and N. Merhav. In their model they assumed that

(1) the attacker uses a single channel to attack the watermark and both,the information hider and the decoder, know the attack channel;

(2) the decoder either completely he knows the covertext or knows nothing about it.

Then instead of the first assumption they suggested to study more robust models and instead of the second assumption they suggested to consider the case where the information hider is allowed to send a secret key to the decoder according to the covertext.

In response to the first suggestion 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. In response to the second suggestion 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. To obtain our lower bounds we introduce the corresponding models of common randomness. 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.