The Round Functions of RIJNDAEL Generate the Alternating Group

Wernsdorf, Ralph

doi:10.1007/3-540-45661-9_11

Cited by 30 publications

(35 citation statements)

References 4 publications

(5 reference statements)

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“…It is has been shown that the round functions of the AES [8,20] generate the alternating group on the state space of the AES [26]. Similar results have been demonstrated for other well-known block ciphers [24,9,25].…”

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

confidence: 56%

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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: 56%

“…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: 83%

Projective aspects of the AES inversion

Jackson

Murphy

2007

Des Codes Crypt

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“…If DES were a group it would have serious consequences on the security of DES, because it means that triple DES would not really be more secure than DES. Luckily it was concluded that DES is not a group [5] (for AES see [34]). However, as we will explain now, the question of such attacks on triple DES remains widely open.…”

Section: Consequences For Block Cipher Cryptanalysismentioning

confidence: 99%

The Inverse S-Box, Non-linear Polynomial Relations and Cryptanalysis of Block Ciphers

Courtois¹

2005

Advanced Encryption Standard – AES

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Abstract. This paper is motivated by the design of AES. We consider a broader question of cryptanalysis of block ciphers having very good non-linearity and diffusion. Can we expect anyway, to attacks such ciphers, clearly designed to render hopeless the main classical attacks ? Recently a lot of attention have been drawn to the existence of multivariate algebraic relations for AES (and other) S-boxes. Then, if the XSL-type algebraic attacks on block ciphers [11] are shown to work well, the answer would be positive. In this paper we show that the answer is certainly positive for many other constructions of ciphers. This is not due to an algebraic attack, but to new types of generalised linear cryptanalysis, highly-nonlinear in flavour. We present several constructions of somewhat special practical block ciphers, seemingly satisfying all the design criteria of AES and using similar S-boxes, and yet being extremely weak. They can be generalised, and evolve into general attacks that can be applied -potentially -to any block cipher.

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“…The simplicity of Rijndael was emphasized by its designers [7,8], and much work has concentrated on the structural properties of the cipher [9,11,15,19,20,23,24].…”

Section: Previous Work and Notationmentioning

confidence: 99%

Essential Algebraic Structure within the AES

Murphy

Robshaw

2002

Lecture Notes in Computer Science

121

135

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Abstract. One difficulty in the cryptanalysis of the Advanced Encryption Standard AES is the tension between operations in the two fields GF (2 8 ) and GF (2). This paper outlines a new approach that avoids this conflict. We define a new block cipher, the BES, that uses only simple algebraic operations in GF ( 2 8 ). Yet the AES can be regarded as being identical to the BES with a restricted message space and key space, thus enabling the AES to be realised solely using simple algebraic operations in one field GF ( 2 8 ). This permits the exploration of the AES within a broad and rich setting. One consequence is that AES encryption can be described by an extremely sparse overdetermined multivariate quadratic system over GF (2 8 ), whose solution would recover an AES key.

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The Round Functions of RIJNDAEL Generate the Alternating Group

Cited by 30 publications

References 4 publications

Projective aspects of the AES inversion

Projective aspects of the AES inversion

The Inverse S-Box, Non-linear Polynomial Relations and Cryptanalysis of Block Ciphers

Essential Algebraic Structure within the AES

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