We introduce C, a practical provably secure block cipher with a slow key schedule. C is based on the same structure as AES but uses independent random substitution boxes instead of a fixed one. Its key schedule is based on the Blum-Blum-Shub pseudo-random generator, which allows us to prove that all obtained security results are still valid when taking into account the dependencies between the round keys. C is provably secure against several general classes of attacks. Strong evidence is given that it resists an even wider variety of attacks. We also propose a variant of C with simpler substitution boxes which is suitable for most applications, and for which security proofs still hold.