For example, some well chosen permutations such as the inverse S-box (Courtois 2005) were chosen to resist basic attacks on block ciphers, which is how the AES S-box has been chosen and standardised. We have abundant literature about how permutations in block ciphers (S-boxes) can be weak or strong. It is important to see that our problem is not quite the same as with block ciphers. What is more, the difference is actually visible and detectable. In this article we will show that many historical cipher machines already had carefully chosen components which do satisfy some properties, which make them systematically, substantially different than a random permutation. This question is however inevitably older. 2003 Meyer and Vaudenay 2017) and later for AES etc. Likewise the question was studied for DES (cf. (Courtois, Drobick, and Schmeh 2018) and (Courtois et al. For the Cold War T-310 block cipher there was a question of a “long-term key” cf. Permutations implemented by the Enigma rotors represent a natural equivalent of these blocks, however we are not aware of any contemporary study of their selection process and security.įor block ciphers, this problem was carefully studied ever since the 1970s. In contemporary cryptology considerable attention is paid to the design criteria for block cipher functional components. A broader question is the design criteria for cryptographic components: how a long term cryptographic setup is generated, selected and approved for official use.
We would like to know how a permutation inside a rotor was made or decided. However we are asking questions deeper than recovering the connections of the rotors. The main question we study here, is a form of reverse engineering of Enigma, which was previously studied very carefully by Rejewski in the 1930s and by Turing, cf.
However, very clearly most rotors are NOT random permutations as we are going to show in this article. This was also what Hebern recommended explicitly in the 1920s. All works on cryptanalysis of Enigma known to the authors, from the 1930s until now, have assumed that rotors are just permutations and do not exhibit any particular weakness or internal structure.
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