Imprimitive permutations groups generated by the round functions of key-alternating block ciphers and truncated differential cryptanalysis
<|reference_start|>Imprimitive permutations groups generated by the round functions of key-alternating block ciphers and truncated differential cryptanalysis: We answer a question of Paterson, showing that all block systems for the group generated by the round functions of a key-alternating block cipher are the translates of a linear subspace. Following up remarks of Paterson and Shamir, we exhibit a connection to truncated differential cryptanalysis.   We also give a condition that guarantees that the group generated by the round functions of a key-alternating block cipher is primitive. This applies in particular to AES.<|reference_end|>
@article{caranti2006imprimitive,
    title={Imprimitive permutations groups generated by the round functions of
  key-alternating block ciphers and truncated differential cryptanalysis},
    author={A. Caranti, F. Dalla Volta, M. Sala, F. Villani},
    journal={arXiv preprint arXiv:math/0606022},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0606022},
    primaryClass={math.GR cs.CR}
}