A Simple Algebraic Representation of Rijndael

Ferguson, Niels; Schroeppel, Richard; Whiting, Doug

doi:10.1007/3-540-45537-x_8

Cited by 93 publications

(61 citation statements)

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“…We have not found any compact (polynomial) representation of round function of 3D (over GF(2 8 )), or of its round components which leads to an effective attack (to the full 22-round 3D). We do not consider expressions such as in [14], which although compact, did not lead to an effective attack on AES. Analogously, because of the non-linear order of the S-box, we do not expect higher-order differential attacks [23,25] to succeed against 3D.…”

Section: Interpolation Higher-order Differential and χ 2 Attacksmentioning

confidence: 99%

“…A 4.75-round impossible differential distinguisher of 3D is depicted in (14), where 'Δ' denotes a nonzero byte difference, '0' denotes a zero byte difference, and '?' denotes an unknown difference (can be zero or not).…”

Section: Impossible Differential Analysismentioning

confidence: 99%

“…denotes an unknown difference (can be zero or not). There are two truncated differentials in (14) that hold with certainty, one in the encryption direction,…”

Section: Impossible Differential Analysismentioning

confidence: 99%

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3D: A Three-Dimensional Block Cipher

Nakahara

2008

Cryptology and Network Security

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Abstract. The main contribution of this paper is a new iterated secretkey block cipher called 3D, inspired by the AES cipher. The 3D cipher has an SPN design, operates on 512-bit blocks, uses 512-bit keys, iterates 22 rounds, and employs a 3-dimensional state, instead of the 2-dimensional matrix of the AES. The main innovation of 3D includes the multi-dimensional state, generalizing the design of Rijndael, and allowing block sizes beyond the 256-bit boundary. This features motivates the use of 3D as a building block for compression functions in hash functions, MAC and stream cipher constructions requiring large internal states. We explain the design decisions and discuss the security of 3D under several attack settings.

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Section: Interpolation Higher-order Differential and χ 2 Attacksmentioning

confidence: 99%

Section: Impossible Differential Analysismentioning

confidence: 99%

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3D: A Three-Dimensional Block Cipher

Nakahara

2008

Cryptology and Network Security

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“…Fixed S-box permits attackers to study the S-box and find frail points, while changing the S-box for each round will makes it tougher for attacker to do any offline analysis of an attack of one particular set of S-boxes [6]. However, overall performance in terms of security and speed has not been sufficiently addressed and widely investigated [13].…”

Section: Properties Of Determinantsmentioning

confidence: 99%

Modified AES S-Box Based on Determinant Matrix Algorithm

et al. 2017

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Abstract-There are many researches in designing and enhancing Rijndael, since it has been chosen as AES. The Sbox is the only nonlinear part in the symmetric encryption algorithms and it defines the performance of AES. In this paper, we propose a new stage named as DeterminantRotation (DR) in modifying and generates different S-box for each round by implementing determinant matrix calculation in rotating the position of AES S-box to be used in the SubBytes transformation. The randomness test and the avalanche test were performed on the output produced in order to prove the security of the new proposed algorithm. The result of the tests shows that the proposed algorithm in the new extra stage has good randomness as well as proven to be secured. Keywords-block cipher, algorithm, AES, determinant, rotation, randomness, avalanche I. INTRODUCTIONCryptography and encryption technique is one of the most proficient approaches employed in order to secure and protect the non-secure channels from attackers. Since Rijndael block cipher or AES (Advanced Standard Encryption) has been announced and adopted by the US government to be used widely as a standard encryption algorithm, there are many other encryption algorithms being develop to fulfil the requirement of secure block cipher. AES is a very robust algorithm that has shown resistance towards many cryptographic attacks so far. It is a symmetric block cipher that can process 128 bits of data blocks using 128, 192 or 256 bits of cryptographic keys. Basically, the block cipher consists of a sequence of identical rounds with each of the round operating under a round key computed from the key.Numerous efforts have been done in redesigning and reconstructing the AES algorithm in order to improve its performance. There are many methods used by researchers in the design and modification of AES block cipher in order to enhance the security of the algorithm as in . Since the AES original S-box has been designed and tested thoroughly for linear and differential attack, attempt on substituting the original S-box without detailed analysis may violate the security of AES original design. This paper introduces a new approach, DeterminantRotation (DR) in modifying and generates different AES S-box each round by implementing determinant matrix calculation in rotating the position of AES S-box to be used in the SubBytes transformation. The aim of this paper is to modify the original AES Sbox in terms of the position of state for each round and to generate different S-box to be used in each round without risking the security properties of a block cipher algorithm.

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“…It is noteworthy that there exists a clear trend in direction of lightweight and fast key-schedule algorithms, as well as substitution boxes based on purely algebraic constructions. In a parallel way, we observe that, on the one hand, several of the last published attacks against block ciphers take often advantage of exploiting "simple" key-schedule algorithms (a nice illustration is certainly Muller's attack [24] against Khazad), and, on the other hand, algebraic S-boxes are helpful to Courtois-Pieprzyk algebraic attacks [8], and lead to puzzling properties as shown by [2,10,25].…”

Section: Introductionmentioning

confidence: 99%

FOX : A New Family of Block Ciphers

Junod

Vaudenay

2004

Lecture Notes in Computer Science

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Abstract. In this paper, we describe the design of a new family of block ciphers based on a Lai-Massey scheme, named FOX. The main features of this design, besides a very high security level, are a large implementation flexibility on various platforms as well as high performances. In addition, we propose a new design of strong and efficient key-schedule algorithms. We provide evidence that FOX is immune to linear and differential cryptanalysis, and we discuss its security towards integral cryptanalysis, algebraic attacks, and other attacks.

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A Simple Algebraic Representation of Rijndael

Cited by 93 publications

References 1 publication

3D: A Three-Dimensional Block Cipher

3D: A Three-Dimensional Block Cipher

Modified AES S-Box Based on Determinant Matrix Algorithm

FOX : A New Family of Block Ciphers

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