Abstract
In each of the 16 DES rounds we have a permutation of 64-bitblocks. According to the corresponding key-block there are 248 possible permutations per round. In this paper we will prove that these permutations generate the alternating group. The main parts of the paper are the proof that the generated group is 3-transitive, and the application of a result from P. J. Cameron based on the classification of finite simple groups. A corollary concerning n-round functions generalizes the result.
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References
Cameron, P. J.: “Finite Permutation Groups and Finite Simple Groups” Bull. London Math. Soc., 13, 1981, 1–22
Cameron, P. J.: Cannon, J.: “Fast Recognition of Doubly Transitive Groups” Journal of Symbolic Computation, 12, Nr. 4&5, 1991, 459–474
Chaum, D.; Evertse, J. H.: “Cryptanalysis of DES with a reduced number of rounds; Sequences of linear factors in blockciphers” Proc. CRYPTO’ 85, Lect. Notes Comp. Sci., 218, 1986, 192–211
Coppersmith, D.; Grossman, E.: “Generators for certain alternating groups with applications to cryptography” Journal of Applied Mathematics, 29, Nr. 4, 1975, 624–627
Davio, M.; Desmedt, Y.: Fosseprez, M. et al.: “Analytical Characteristics of the DES” Proc. CRYPTO’ 83, Plenum Press, New York and London, 1984, 171–202
Even, S.; Goldreich, O.: “DES-like functions can generate the alternating group” IEEE Transactions on Information Theory, IT-29, Nr. 6, 1983, 863–865
Kaliski, B. S.; Rivest, R. L.; Sherman, A. T.: “Is the Data Encryption Standard a Group? (Results of Cycling Experiments on DES)” Journal of Cryptology, 1, Nr. 1, 1988, 3–36
National Bureau of Standards: “Data Encryption Standard” FIPS PUB 46, Washington, 1977
Pieprzyk, J.; Zhang, X. M.: “Permutation Generators of Alternating Groups” Proc. AUSCRYPT’ 90, Lect. Notes Comp. Sci., 453, 1990, 237–244
Reeds, J. A.; Manferdelli, J. L.: “DES has no per round linear factors” Proc. CRYPTO’ 84, Lect. Notes Comp. Sci., 196, 1985, 377–389
Robinson, D. J. S.: “A Course in the Theory of Groups” Springer, New York, Heidelberg, Berlin, 1982
Simmons, G. J.; Moore, J. H.: “Cycle structure of the DES for keys having palindromic (or antipalindromic) sequences of round keys” IEEE Transactions on Software Engineering, SE-13, Nr. 2, 1987, 262–273
Wielandt, H.: “Finite Permutation Groups” Academic Press, New York, London, 1964
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© 1993 Springer-Verlag Berlin Heidelberg
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Wernsdorf, R. (1993). The One-Round Functions of the DES Generate the Alternating Group. In: Rueppel, R.A. (eds) Advances in Cryptology — EUROCRYPT’ 92. EUROCRYPT 1992. Lecture Notes in Computer Science, vol 658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47555-9_9
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DOI: https://doi.org/10.1007/3-540-47555-9_9
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