We propose the
framework with goal to unify the design of tweakable block ciphers and of block ciphers resistant to related-key attacks. Our framework is simple, extends the key-alternating construction, and allows to build a primitive with arbitrary tweak and key sizes, given the public round permutation (for instance, the
round). Increasing the sizes renders the security analysis very difficult and thus we identify a subclass of
, that we name
, which solves the size issue by the use of finite field multiplications on low hamming weight constants. Overall, this construction allows a significant increase of security of well-known authenticated encryptions mode like Θ
from birthday-bound security to full security, where a regular block cipher was used as a black box to build a tweakable block cipher. Our work can also be seen as advances on the topic of secure key schedule design.