  We initiate the provable related-key security treatment for models of
practical Feistel ciphers. In detail, we consider Feistel networks with four
whitening keys $w_i(k)$ ($i=0,1,2,3$) and round-functions of the form
$f(\gamma_i(k)\oplus X)$, where $k$ is the main-key, $w_i$ and $\gamma_i$ are
efficient transformations, and $f$ is a public ideal function or permutation
that the adversary is allowed to query. We investigate conditions on the
key-schedules that are sufficient for security against XOR-induced related-key
attacks up to $2^{n/2}$ adversarial queries. When the key-schedules are
non-linear, we prove security for 4 rounds. When only affine key-schedules are
used, we prove security for 6 rounds. These also imply secure tweakable Feistel
ciphers in the Random Oracle model.
  By shuffling the key-schedules, our model unifies both the DES-like structure
(known as Feistel-2 scheme in the cryptanalytic community, a.k.a.
key-alternating Feistel due to Lampe and Seurin, FSE 2014) and the Lucifer-like
model (previously analyzed by Guo and Lin, TCC 2015). This allows us to derive
concrete implications on these two (more common) models, and helps
understanding their differences---and further understanding the related-key
security of Feistel ciphers.
