The paper "On the group generated by the round functions of translation based ciphers over arbitrary finite fields" states:

Definition 3.3. A block cipher $C = \{ \tau_k | k ∈ K \}$ over $F_q$ is called translation based (tb) if:

  1. each $\tau_k$ is the composition of $l$ round functions $\tau_{k,h}$ , for $k ∈ K$, and $h = 1, . . . , l$, where in turn each round function $\tau_{k,h}$ can be written as a composition $\gamma_h\lambda_h\sigma_{φ(k,h)}$ of three permutations of $V$ , where:

    • $\gamma_h$ is a bricklayer transformation not depending on $k$ and $0\gamma_h = 0$
    • $\lambda_h$ is a linear permutation not depending on $k$,
    • $φ : K × \{1, . . ., l\}→ V$ is the key scheduling function, so that $φ (k, h)$ is the $h$-th round key, given the master key $k$;
  2. for at least one round index $h_0$ we have that

    • $\lambda_{h_0}$ is a proper mixing layer, and
    • the map $K → V$ given by $k → φ (k, h_0)$ is surjective, that is, every element of $V$ occurs as an $h_0$-th round key

How do I check if this map is surjective? Is AES a translation based block cipher?


1 Answer 1


Well, you probably cannot check this without a somewhat explicit specification of $\varphi.$ In general, if the key scheduling function has a simple structure, and if $|V|=|K|$ this becomes easier; In that case, if $\varphi(h_0,\cdot)$ is a permutation you are done.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.