The group generated by the round functions of a GOST-like cipher
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We define a cipher that is an extension of GOST, and study the permutation group generated by its round functions. We show that, under minimal assumptions on the components of the cipher, this group is the alternating group on the plaintext space. This we do by first showing that the group is primitive, and then applying the O’Nan-Scott classification of primitive groups.
KeywordsCryptosystems Feistel networks GOST round functions primitive groups wreath products
Mathematics Subject Classification20B15 20B35 94A60
The authors are grateful to the referee for her suggestions. The authors are indebted to Rüdiger Sparr and Ralph Wernsdorf for reading a previous version and suggesting several changes, pointing out in particular a serious oversight on our part regarding the parity of permutations and providing a shorter argument for Sect. 5.3.
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