Side channels are communication channels that were not intended for communication and that accidentally leak information. A storage side channel leaks information through the content of the channel and not its timing behavior. Storage side channels are a large problem in networked applications since the output at the level of the protocol encoding (e.g., HTTP and HTML) often depends on data and control flow. We call such channels hidden because the output differences blend with the noise of the channel. Within a formal system model, we give a necessary and sufficient condition for such storage side channels to exist. Based on this condition, we develop a method to detect this kind of side channels. The method is based on systematic comparisons of network responses of web applications. We show that this method is useful in practice by exhibiting hidden storage side channels in three well-known web applications: Typo3, Postfix Admin, and Zenith Image Gallery