Codes, graphs, and schemes from nonlinear functions

Dam, E.R. van; Fon-Der-Flaass, D. G.

doi:10.1016/s0195-6698(02)00116-6

Cited by 32 publications

(30 citation statements)

References 14 publications

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“…We also point out that, besides their cardinalities, the algebraic structures of the image sets of the derivatives of the inverse permutation are of great importance, in particular the case where these sets are affine subspaces is the most favourable one for the attacker. In other words, we show that the use of APN permutations satisfying the crooked property [vDdF00,BdF98] makes the primitive very weak in the context of Maraca. This also leads us to introduce a natural generalization of the crooked property in the light of our attack, which captures the functions with a higher differential uniformity and a higher nonlinearity.…”

Section: Introductionmentioning

confidence: 90%

“…A very particular case has been investigated in [BdF98,vDdF00] where the notion of crooked permutations have been introduced. Here, we recall this notion in the more general sense defined by Kyureghyan [Kyu07] which also includes the case where the function is not a permutation, and then where Im(D β F ) is a linear subspace of codimension 1.…”

Section: Algebraic Structure Of D F (δ) and Generalized Crooked Functmentioning

confidence: 99%

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Structural weaknesses of permutations with a low differential uniformity and generalized crooked functions

Canteaut¹,

Naya-Plasencia²

2010

Finite Fields: Theory and Applications

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Abstract. Any permutation with a low differential uniformity is shown to be such that its inverse has a derivative with a large image set. An attack exploiting this structural property is then presented against a recent hash function proposal, named Maraca, submitted to the SHA-3 competition. Moreover, the attack can be made much more efficient when the image sets of the derivatives of the inverse permutation are affine subspaces. This cryptanalytic approach leads to some generalizations of the notion of crooked functions, and to the study of their properties.

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Section: Introductionmentioning

confidence: 90%

Section: Algebraic Structure Of D F (δ) and Generalized Crooked Functmentioning

confidence: 99%

Structural weaknesses of permutations with a low differential uniformity and generalized crooked functions

Canteaut¹,

Naya-Plasencia²

2010

Finite Fields: Theory and Applications

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“…Besides of applications in cryptology, APN mappings yield optimal objects in finite geometry, combinatorics and coding theory, cf. [29,58,61,95,100,101]. An interesting connection between APN mappings and reversed Dickson polynomials is given in [68].…”

Section: Almost Perfect Nonlinear (Apn) Mappingsmentioning

confidence: 99%

Special Mappings of Finite Fields

Kyureghyan¹

2013

Finite Fields and Their Applications

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Mappings of finite fields play an important role in many applications like coding theory, combinatorics, cryptology or finite geometry. In this article we survey recent progress on classification and explicit constructions of almost perfect nonlinear, bent, crooked mappings and those having a linear structure. We present the switching method, which proved itself as a powerful tool for constructing mappings satisfying additive properties. We describe main open challenges in this research area.

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“…Several interesting problems and conjectures arise from the study of non-linearity of polynomials and more specially in the case of monomials also called power functions. Questions that come from different frameworks: cyclic codes with two zeroes, correlation of sequences, Boolean functions and graphs theory [9]. See [2] for a complete list of references.…”

Section: Non-linearitymentioning

confidence: 99%