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Notions and relations for RKA-secure permutation and function families
The theory of designing block ciphers is mature, having seen signi¯cant
progress since the early 1990s for over two decades, especially during the AES devel-
opment e®ort. Nevertheless, interesting directions exist, in particular in the study of
the provable security of block ciphers along similar veins as public-key primitives, i.e.
the notion of pseudorandomness (PRP) and indistinguishability (IND). Furthermore,
recent cryptanalytic progress has shown that block ciphers well designed against known
cryptanalysis techniques including related-key attacks (RKA) may turn out to be less
secure against related-key attacks than expected. The notion of provable security of
block ciphers against related-key attacks was initiated by Bellare and Kohno, and sub-
sequently treated by Lucks. Concrete block cipher constructions were proposed therein
with provable security guarantees. In this paper, we are interested in the security no-
tions for RKA-secure block ciphers