ZUC is a stream cipher used for encryption in 4G and 5G communications
which is composed of an LFSR (Linear Feedback Shift Register) over
$\mathbb{F}_{2^{31}-1}$ and an FSM (Final State Machine) over a binary
field.\\

Although the algorithm is widely used, classical attacks on stream
ciphers such as fast correlation attacks are difficult to evaluate on it
due to its particular structure including operations over different
fields. Thus even if correlations exist between the output of the cipher
and its internal state, making the link between fields with different
characteristics was still left as an open problem.\\

In this work we find a way to compute the probabilities of propagating
masks from a binary field to a non binary field and we give the first
key-recovery attack on the keystream generation of ZUC-256 with data and
time complexity below $2^{256}$.