Generalized Boolean Bent Functions

Poinsot, Laurent; Harari, Sami

doi:10.1007/978-3-540-30556-9_10

Cited by 5 publications

(9 citation statements)

References 4 publications

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“…1, we will consider a different group action on the bits than XOR. The generalized differential attack motivates our need to balance the outputs based on the group action, leading to the following definition [27][28][29]. Definition 3.1 Let G and H be groups, let X be a finite nonempty set with G acting faithfully on X via the homomorphism φ, and let f :…”

Section: Group Action Approachmentioning

confidence: 99%

G-Perfect nonlinear functions

Davis¹,

Poinsot²

2007

Des. Codes Cryptogr.

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Perfect nonlinear functions are used to construct DES-like cryptosystems that are resistant to differential attacks. We present generalized DES-like cryptosystems where the XOR operation is replaced by a general group action. The new cryptosystems, when combined with G-perfect nonlinear functions (similar to classical perfect nonlinear functions with one XOR replaced by a general group action), allow us to construct systems resistant to modified differential attacks. The more general setting enables robust cryptosystems with parameters that would not be possible in the classical setting. We construct several examples of G-perfect nonlinear functions, both Z 2 -valued and Z a 2 -valued. Our final constructions demonstrate G-perfect nonlinear planar permutations (from Z a 2 to itself), thus providing an alternative implementation to current uses of almost perfect nonlinear functions.Keywords G-perfect nonlinear functions · Difference sets AMS Classifications 05B10 · 11T71 Background on cryptosystems and group action modificationsIn an r-round iterative block cipher such as the Data Encryption Standard (DES) [17] or the Advanced Encryption Standard (AES) [9,18] the ciphertext x r is obtained from a plaintext x 0 by r iterations of the round function f

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Section: Group Action Approachmentioning

confidence: 99%

G-Perfect nonlinear functions

Davis¹,

Poinsot²

2007

Des. Codes Cryptogr.

Self Cite

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“…It is shown in [50] that every group of involutions G of Z k 2 is abelian and |G| 2 k . We consider only a group G of the maximal order 2 k .…”

Section: Vector G-bent Functionsmentioning

confidence: 99%

“…A simple example of this group is the translation group T Z k 2 consisting of all permutations σ y , y ∈ Z k 2 , such that σ y (x) = x + y. However, other maximal groups of involutions exist [50].…”

Section: Vector G-bent Functionsmentioning

confidence: 99%

“…A translation of the definition of G-bent functions into the language of generalized Fourier coefficients is proposed in [50], but so far it fails to appear thoroughly worked out and includes inaccuracies. Also it is unclear to what extent the approach of [50] applies if A and B are arbitrary abelian groups.…”

Section: Vector G-bent Functionsmentioning

confidence: 99%

“…Also it is unclear to what extent the approach of [50] applies if A and B are arbitrary abelian groups.…”

Section: Vector G-bent Functionsmentioning

confidence: 99%

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