This article proposes a theory of watermarking security based on a cryptanalysis point of view. The main idea is that information about the secret key leaks from the observations, for instance watermarked pieces of content, available to the opponent. Tools from information theory (Shannon's mutual information and Fisher's information matrix) can measure this leakage of information. The security level is then defined as the number of observations the attacker needs to successfully estimate the secret key. This theory is applied to two common watermarking methods: the substitutive scheme and the spread spectrum based techniques. Their security levels are calculated against three kinds of attack. The experimental work illustrates how Blind Source Separation (especially Independent Component Analysis) algorithms help the opponent exploiting this information leakage to disclose the secret carriers in the spread spectrum case. Simulations assess the security levels derived in the theoretical part of the article.