Key-Alternating Feistel (KAF) ciphers are a popular variant of Feistel ciphers whereby the round functions are defined as x↦F(ki⊕x), where k_i are the round keys and F is a public random function. Most Feistel ciphers, such as DES, indeed have such a structure. However, the security of this construction has only been studied in the classical CPA/CCA models. We provide the first security analysis of KAF ciphers in the key-dependent message (KDM) attack model, where plaintexts can be related to the private key. This model is motivated by cryptographic schemes used within application scenarios such as full-disk encryption or anonymous credential systems. We show that the four-round KAF cipher, with a single function F reused across the rounds, provides KDM security for a non-trivial set of KDM functions. To do so, we develop a generic proof methodology, based on the H-coefficient technique, that can ease the analysis of other block ciphers in such strong models of security.