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This article is a theoretical study on binary Tardos' fingerprinting codes embedded using watermarking schemes. Our approach is derived from and encompasses both security and robustness constraints. We assume here that the coalition has estimated the symbols of the fingerprinting code by the way of a security attack, the quality of the estimation relying on the security of the watermarking scheme. Taking into account the fact that the coalition can perform estimation errors, we update the Worst Case Attack, which minimises the mutual information between the sequence of one colluder and the pirated sequence forged by the coalition. After comparing the achievable rates of the previous and proposed Worst Case Attack according to the estimation error, we conclude this analysis by comparing the robustness of no-secure embedding schemes versus secure ones. We show that, for low probabilities of error during the decoding stage (e.g. highly robust watermarking schemes), security enables to increase the achievable rate of the fingerprinting scheme.