The One-Round Functions of the DES Generate the Alternating Group

Wernsdorf, Ralph

doi:10.1007/3-540-47555-9_9

Cited by 35 publications

(30 citation statements)

References 10 publications

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“…Similar results have been demonstrated for other well-known block ciphers [24,9,25]. It is of course possible to construct block ciphers whose round functions generate the alternating or symmetric group, but are easy to attack by exploiting statistical properties of the block cipher [17].…”

Section: Introduction To the Group-theoretic Properties Of A Ciphersupporting

confidence: 78%

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Projective aspects of the AES inversion

Jackson

Murphy

2007

Des Codes Crypt

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Abstract. We consider the nonlinear function used in the Advanced Encryption Standard (AES). This nonlinear function is essentially inversion in the finite field GF(2 8 ), which is most naturally considered as a projective transformation. Such a viewpoint allows us to demonstrate certain properties of this AES nonlinear function. In particular, we make some comments about the group generated by such transformations, and we give a characterisation for the values in the AES Difference or XOR Table for the AES nonlinear function and comment on the geometry given by this XOR Table.

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Section: Introduction To the Group-theoretic Properties Of A Ciphersupporting

confidence: 78%

“…We have discussed the group generated by the set of AES-like transformations acting on the state space F in a similar manner to the discussions given in [24,9,25,26]. We have shown that the group generated by the AES-like transformations is generally the symmetric group on Sym(F).…”

Section: Comments On the "Group Generated By A Cipher"mentioning

confidence: 84%

Projective aspects of the AES inversion

Jackson

Murphy

2007

Des Codes Crypt

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“…-Direct application of these techniques to existing block ciphers such as DES is not expected to be fruitful because it is known that keys of nonzero probability are sparse in a large group. Furthermore, it took several decades of open research to establish (finally in [23]) the precise group for DES. Nevertheless, in the design of new ciphers, the group G is easily treated as a design parameter.…”

Section: Resultsmentioning

confidence: 99%

Guesswork and Variation Distance as Measures of Cipher Security

Pliam

2000

Lecture Notes in Computer Science

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Abstract. Absolute lower limits to the cost of cryptanalytic attacks are quantified, via a theory of guesswork. Conditional guesswork naturally expresses limits to known and chosen plaintext attacks. New inequalities are derived between various forms of guesswork and variation distance. The machinery thus offers a new technique for establishing the security of a cipher: When the work-factor of the optimal known or chosen plaintext attack against a cipher is bounded below by a prohibitively large number, then no practical attack against the cipher can succeed.As an example, we apply the technique to iterated cryptosystems, as the Markov property which results from an independent subkey assumption makes them particularly amenable to analysis.

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“…Further work on this theme can be found in [26]. In [30] it was shown that the actual round functions of DES generate the alternating group. The question of whether the 2 56 encryptions of the full DES algorithm themselves form a group, or generate a small group (see [13,23]), was answered in the negative in [5] and a lower bound of 10 2499 was obtained in [4] for the size of this generated group.…”

Section: Introductionmentioning

confidence: 99%

“…Consider the following statement of Wernsdorf [30] regarding the group generated by the round functions of DES:…”

Section: Introductionmentioning

confidence: 99%

Imprimitive Permutation Groups and Trapdoors in Iterated Block Ciphers

Paterson

1999

Fast Software Encryption

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Abstract. An iterated block cipher can be regarded as a means of producing a set of permutations of a message space. Some properties of the group generated by the round functions of such a cipher are known to be of cryptanalytic interest. It is shown here that if this group acts imprimitively on the message space then there is an exploitable weakness in the cipher. It is demonstrated that a weakness of this type can be used to construct a trapdoor that may be difficult to detect. An example of a DES-like cipher, resistant to both linear and differential cryptanalysis that generates an imprimitive group and is easily broken, is given. Some implications for block cipher design are noted.

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The One-Round Functions of the DES Generate the Alternating Group

Cited by 35 publications

References 10 publications

Projective aspects of the AES inversion

Projective aspects of the AES inversion

Guesswork and Variation Distance as Measures of Cipher Security

Imprimitive Permutation Groups and Trapdoors in Iterated Block Ciphers

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