Classifying 8-Bit to 8-Bit S-Boxes Based on Power Mappings from the Point of DDT and LAT Distributions

Aslan, Bora; Sakallı, Muharrem Tolga; Buluş, Ercan

doi:10.1007/978-3-540-69499-1_11

Cited by 12 publications

(5 citation statements)

References 15 publications

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“…From Equation (8), it is clear to see that if the A-I matrix has bigger rank, then the linear transformation A has the less number of fixed points. In [13], the diffusion measure based on the number of fixed points is applied to the linear transformations of several SPN ciphers: the AES, ARIA, PRESENT [28], and Serpent [29].…”

Section: Fixed Points In Linear Transformationsmentioning

confidence: 99%

“…. ., f 0 are in GF(2 8 ), then we obtain a 64-bit to a 64-bit linear transformation with good cryptographic properties.…”

Section: Algebraic Construction Of 8 â 8 Binary Linear Transformationsmentioning

confidence: 99%

“…(1) Be MDS, (2) Be involutory and random matrix given in Lemma 4, (3) The binary matrix, A Binary , transformed from 2 Â 2 matrix should have branch number of 5 and the rank of A Binary À I matrix will be 4. Therefore, if it is used as a 64-bit to a 64-bit linear transformation, where each input element is in GF(2 8 ), the binary linear transformation will have 2 32 fixed points.…”

Section: Algebraic Construction Of 8 â 8 Binary Linear Transformationsmentioning

confidence: 99%

“…The substitution layer or nonlinear layer ensures that this dependency is of a complex and nonlinear nature [4], [5]. Popular choices of substitution layers or S-boxes providing good cryptographic properties are based on inversion mapping over GF (2 8 ) [6], [7], [8], [9]. Such S-boxes are widely used in block ciphers like the AES, Camellia [10], and ARIA [11].…”

Section: Introductionmentioning

confidence: 99%

“…Also, it uses an 8 Â 8 non-involutory binary matrix over GF (2 8 ) as a diffusion layer. On the other hand, the AES uses a 4 Â 4 non-involutory MDS matrix over GF (2 8 ), which transforms a 32-bit input to a 32-bit output.…”

Section: Introductionmentioning

confidence: 99%

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Algebraic construction of cryptographically good binary linear transformations

Aslan

Sakallı

2012

Security Comm. Networks

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Maximum Distance Separable (MDS) and Maximum Distance Binary Linear (MDBL) codes are used as diffusion layers in the design of the well-known block ciphers like the Advanced Encryption Standard, Khazad, Camellia, and ARIA. The reason for the use of these codes in the design of block ciphers is that they provide optimal diffusion effect to meet security of a round function of a block cipher. On the other hand, the constructions of these diffusion layers are various. For example, whereas the Advanced Encryption Standard uses a 4 Â 4 MDS matrix over GF(2 8 ), ARIA uses a 16 Â 16 involutory binary matrix over GF(2 8 ). The most important cryptographic property of a diffusion layer is the branch number of that diffusion layer, which represents the diffusion rate and measures security against linear and differential cryptanalysis. Therefore, MDS and Maximum Distance Binary Linear codes, which provide maximum branch number for a diffusion layer, are preferred in the design of block ciphers as diffusion layers. In this paper, we present a new algebraic construction method based on MDS codes for 8 Â 8 and 16 Â 16 involutory and non-involutory binary matrices of branch numbers 5 and 8, respectively. By using this construction method, we also show some examples of these diffusion layers.

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Section: Fixed Points In Linear Transformationsmentioning

confidence: 99%

“…. ., f 0 are in GF(2 8 ), then we obtain a 64-bit to a 64-bit linear transformation with good cryptographic properties.…”

Section: Algebraic Construction Of 8 â 8 Binary Linear Transformationsmentioning

confidence: 99%

Section: Algebraic Construction Of 8 â 8 Binary Linear Transformationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Algebraic construction of cryptographically good binary linear transformations

Aslan

Sakallı

2012

Security Comm. Networks

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Relationships Between CCZ and EA Equivalence Classes and Corresponding Code Invariants

Horadam

Villanueva

2014

Sequences and Their Applications - SETA 2014

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Abstract. The purpose of this paper is to provide a brief survey of CCZ and EA equivalence for functions f : G → N where G and N are finite and N is abelian, and, for the case f : Z m p → Z m p , to investigate two codes derived from f , inspired by these equivalences. In particular we show the dimension of the kernel of each code determines a new invariant of the corresponding equivalence class. We present computational results for p = 2 and small m.

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