Special Mappings of Finite Fields

Kyureghyan, Gohar M.

doi:10.1515/9783110283600.117

Cited by 6 publications

(2 citation statements)

References 71 publications

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“…And it is highly conjectured that the crooked functions exactly correspond to the quadratic APN functions. This has been proved in [30] in the case of monomial functions and in [4] in the case of binomials. Now we can prove the following.…”

Section: B Proofs Of Propositions 4 Andmentioning

confidence: 87%

On the Behaviors of Affine Equivalent Sboxes Regarding Differential and Linear Attacks

Canteaut

Roué

2015

Advances in Cryptology -- EUROCRYPT 2015

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To cite this version:Anne Canteaut, Joëlle Roué. On the behaviors of affine equivalent Sboxes regarding differential and linear attacks. Abstract. This paper investigates the effect of affine transformations of the Sbox on the maximal expected differential probability MEDP and linear potential MELP over two rounds of a substitution-permutation network, when the diffusion layer is linear over the finite field defined by the Sbox alphabet. It is mainly motivated by the fact that the 2-round MEDP and MELP of the AES both increase when the AES Sbox is replaced by the inversion in F 2 8 . Most notably, we give new upper bounds on these two quantities which are not invariant under affine equivalence. Moreover, within a given equivalence class, these new bounds are maximal when the considered Sbox is an involution. These results point out that different Sboxes within the same affine equivalence class may lead to different two-round MEDP and MELP. In particular, we exhibit some examples where the basis chosen for defining the isomorphism between F m 2 and F2m affects these values. For Sboxes with some particular properties, including all Sboxes of the form A(x s ) as in the AES, we also derive some lower and upper bounds for the 2-round MEDP and MELP which hold for any MDS linear layer.

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Section: B Proofs Of Propositions 4 Andmentioning

confidence: 87%

On the Behaviors of Affine Equivalent Sboxes Regarding Differential and Linear Attacks

Canteaut

Roué

2015

Advances in Cryptology -- EUROCRYPT 2015

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“…Since a permutation of F 2 m has degree at most (m − 1), all APN Sboxes over F 8 are quadratic, and their inverses are also quadratic. Therefore, they are crooked [2,18], i.e., for any nonzero a ∈ F 2 3 , the set {b ∈ F 2 3 : δ S F (a, b) = 2} is an affine hyperplane of F 2 3 . Furthermore, it is known that all these affine hyperplanes are distinct [7,Lemma 5].…”

Section: Apn Sboxes Over Fmentioning

confidence: 99%

Differential Attacks Against SPN: A Thorough Analysis

Canteaut

Roué

2015

Lecture Notes in Computer Science

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Abstract. This work aims at determining when the two-round maximum expected differential probability in an SPN with an MDS diffusion layer is achieved by a differential having the fewest possible active Sboxes. This question arises from the fact that minimum-weight differentials include the best differentials for the AES and several variants. However, we exhibit some SPN for which the two-round MEDP is achieved by some differentials involving a number of active Sboxes which exceeds the branch number of the linear layer. On the other hand, we also prove that, for some particular families of Sboxes, the two-round MEDP is always achieved for minimum-weight differentials.

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Almost perfect and planar functions

Pott

2015

Des. Codes Cryptogr.

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Special Mappings of Finite Fields

Cited by 6 publications

References 71 publications

On the Behaviors of Affine Equivalent Sboxes Regarding Differential and Linear Attacks

On the Behaviors of Affine Equivalent Sboxes Regarding Differential and Linear Attacks

Differential Attacks Against SPN: A Thorough Analysis

Almost perfect and planar functions

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