An Algebraic Framework for Cipher Embeddings

Cid, Carlos; Murphy, Seán; Robshaw, Matthew J. B.

doi:10.1007/11586821_19

Cited by 5 publications

(4 citation statements)

References 13 publications

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“…There is a sense in the above construction in which the original state space F is embedded in a larger state space F = F ∪ {∞} with 0 and ∞ being identified when the embedding needs reversing. This is in many ways similar to the general ideas of embedding a block cipher state space algebra in a larger state space algebra discussed in [18,6]. The interesting question when discussing the "group generated by the AES" is whether for the AES there is a similar construction to the above example for the AES state space F 16 (n = 8), but which also gives a smaller and more structured group than the symmetric or alternating group on F 16 .…”

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

confidence: 53%

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: Comments On the "Group Generated By A Cipher"supporting

confidence: 53%

Projective aspects of the AES inversion

Jackson

Murphy

2007

Des Codes Crypt

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“…[5,20]). It is known that "a change of the Rijndael polynomial should not affect the strength of the cipher".…”

Section: Theorem 31 the Set G Is A Gröbner Basis Of A Zero-dimensionmentioning

confidence: 97%

“…Different manipulations and variations of these methods were considered since their appearance. Some works in this area are [1,2,15,16,[18][19][20][21][22]24,35,37,38]. So far no method presented any real threat to AES.…”

Section: Introductionmentioning

confidence: 96%

Obtaining and Solving Systems of Equations in Key Variables Only for the Small Variants of AES

Bulygin

Brickenstein

2010

Math.Comput.Sci.

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This work is devoted to attacking the small scale variants of the Advanced Encryption Standard (AES) via systems that contain only the initial key variables. To this end, we investigate a system of equations that naturally arises in the AES, and then introduce an elimination of all the intermediate variables via normal form reductions. The resulting system in key variables only is solved then. We also consider a possibility to apply our method in the meet-in-the-middle scenario especially with several plaintext/ciphertext pairs. We elaborate on the method further by looking for subsystems which contain fewer variables and are overdetermined, thus facilitating solving the large system.

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“…Our main focus point is to investigate (nonlinear) equivalence of LFSR-based stream ciphers using basic properties of Galois fields and certain isomorphisms between the corresponding multiplicative groups. This can be seen as a way of constructing isomorphic ciphers (examples of cipher representations and isomorphisms were provided in [1,9]; the subject was discussed in detail in [2]). …”

Section: Introductionmentioning

confidence: 99%

Nonlinear Equivalence of Stream Ciphers

Rønjom¹,

Cid

2010

Fast Software Encryption

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Abstract. In this paper we investigate nonlinear equivalence of stream ciphers over a finite field, exemplified by the pure LFSR-based filter generator over F2. We define a nonlinear equivalence class consisting of filter generators of length n that generate a binary keystream of period dividing 2 n −1, and investigate certain cryptographic properties of the ciphers in this class. We show that a number of important cryptographic properties, such as algebraic immunity and nonlinearity, are not invariant among elements of the same equivalence class. It follows that analysis of cipher-components in isolation presents some limitations, as it most often involves investigating cryptographic properties that vary among equivalent ciphers. Thus in order to assess the resistance of a cipher against a certain type of attack, one should in theory determine the weakest equivalent cipher and not only a particular instance. This is however likely to be a very difficult task, when we consider the size of the equivalence class for ciphers used in practice; therefore assessing the exact cryptographic properties of a cipher appears to be notoriously difficult.

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An Algebraic Framework for Cipher Embeddings

Cited by 5 publications

References 13 publications

Projective aspects of the AES inversion

Projective aspects of the AES inversion

Obtaining and Solving Systems of Equations in Key Variables Only for the Small Variants of AES

Nonlinear Equivalence of Stream Ciphers

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