Obtaining and Solving Systems of Equations in Key Variables Only for the Small Variants of AES

Bulygin, Stanislav; Brickenstein, Michael

doi:10.1007/s11786-009-0020-y

Cited by 8 publications

(13 citation statements)

References 25 publications

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“…As mentioned earlier, chaos- and algebraic-based techniques are extensively used to design the confusion component. Chaos- and algebraic-based techniques provide favorable features for the design of confusion components; however, researchers have also identified various cryptanalysis on these techniques including interpolation attacks [ 9 – 12 ], Gröbner basis attack [ 13 – 19 ], SAT solver [ 20 – 27 ], linear and differential attacks [ 28 – 42 ], XL attacks [ 43 – 45 ], and XSL attack [ 9 , 46 – 55 ]. Similarly, chaos-based techniques are also commonly applied in the designs of confusion components [ 56 – 68 ], dynamical degradation of chaotic systems [ 69 – 73 ], predictability [ 74 – 85 ], discontinuity in chaotic sequences [ 70 , 86 – 90 ], small number of control parameters [ 76 , 77 , 91 , 92 ], finite precision effect [ 70 – 72 , 86 , 88 ], and short quantity of randomness [ 71 , 72 , 86 , 88 – 90 , 93 – 96 ].…”

Section: Attacks On Confusion Component Design Schemesmentioning

confidence: 99%

Human Psychological Disorder towards Cryptography: True Random Number Generator from EEG of Schizophrenics and Its Application in Block Encryption’s Substitution Box

Khan

Saleem

Hazzazi

et al. 2022

Computational Intelligence and Neuroscience

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Schizophrenia is a multifaceted chronic psychiatric disorder that affects the way a human thinks, feels, and behaves. Inevitably, natural randomness exists in the psychological perception of schizophrenic patients, which is our primary source of inspiration for this research because true randomness is the indubitably ultimate valuable resource for symmetric cryptography. Famous information theorist Claude Shannon gave two desirable properties that a strong encryption algorithm should have, which are confusion and diffusion in his fundamental article on the theoretical foundations of cryptography. Block encryption strength against various cryptanalysis attacks is purely dependent on its confusion property, which is gained through the confusion component. In the literature, chaos and algebraic techniques are extensively used to design the confusion component. Chaos- and algebraic-based techniques provide favorable features for the design of the confusion component; however, researchers have also identified potential attacks on these techniques. Instead of existing schemes, we introduce a novel methodology to construct cryptographic confusion component from the natural randomness, which are existing in the psychological perception of the schizophrenic patients, and as a result, cryptanalysis of chaos and algebraic techniques are not applicable on our proposed technique. The psychological perception of the brain regions was captured through the electroencephalogram (EEG) readings during the sensory task. The proposed design passed all the standard evaluation criteria and validation tests of the confusion component and the random number generators. One million true random bits are assessed through the NIST statistical test suite, and the results proved that the psychological perception of schizophrenic patients is a good source of true randomness. Furthermore, the proposed confusion component attains better or equal cryptographic strength as compared to state-of-the-art techniques (2020 to 2021). To the best of our knowledge, this nature of research is performed for the first time, in which psychiatric disorder is utilized for the design of information security primitive. This research opens up new avenues in cryptographic primitive design through the fusion of computing, neuroscience, and mathematics.

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Section: Attacks On Confusion Component Design Schemesmentioning

confidence: 99%

Human Psychological Disorder towards Cryptography: True Random Number Generator from EEG of Schizophrenics and Its Application in Block Encryption’s Substitution Box

Khan

Saleem

Hazzazi

et al. 2022

Computational Intelligence and Neuroscience

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“…We apply the degrevlex ordering, where secret key variables have lower order than other variables. We use a similar notation to the one used by Bulygin and Brickenstein [7]. The

S R false(n, 2, 1, 4 false)

cipher is described by the following system of equations:

({, \begin{matrix} 1em4pt \\ s b o x false(p_{0} + k_{0, 0}, x_{0, 0} false) \\ s b o x false(p_{1} + k_{0, 1}, x_{0, 1} false) \\ s b o x false(L_{0} false(x_{i - 1, 0}, x_{i - 1, 1} false) + k_{i, 0}, x_{i, 0} false) & for i = 1, \dots, n \\ s b o x false(L_{1} false(x_{i - 1, 0}, x_{i - 1, 1} false) + k_{i, 1}, x_{i, 1} false) & for i = 1, \dots, n \\ c_{0} + L_{0} false(x_{n, 0}, x_{n, 1} false) + k_{n, 0} \\ c_{1} + L_{1} false(x_{n, 0}, x_{n, 1} false) + k_{n, 1} \\ s b o x false(k_{i, 0}, k_{i + 1, 0} \end{matrix})

…”

Section: Sr Block Ciphersmentioning

confidence: 99%

“…[5] report results of experiments, where cryptanalysis is performed for 4‐bit and 8‐bit versions of an round‐reduced AES using the Gröbner basis algorithm F4 [6]. To our knowledge, the best algebraic cryptanalysis results for this family of ciphers are reported in [7].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, using this representation, we are able to solve system of equations for

S R false(10, 2, 1, 4 false)

with computer algebra packages S ingular [14] and FGb [15], where

S R false(n, r, c, e false)

is a AES variant with n rounds, r is the number of rows, c is the number of columns and e is the size of the word in bits. The analysis reported in [5, 7] uses the F4 algorithm [6] and S ingular . However, for the number of rounds

n \geq 5

, the analysis fails.…”

Section: Introductionmentioning

confidence: 99%

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S‐boxes representation and efficiency of algebraic attack

Arabnezhad-Khanoki¹,

Sadeghiyan²,

Pieprzyk

2019

IET Information Security

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“…S-box designs of pure algebraic structures are jeopardized due to the intrinsic algebraic structure. Various algebraic attacks are available for algebraic construction of S-boxes including linear and differential attacks 3 – 17 , interpolation attacks 18 – 21 , Gröbner basis attack 22 – 28 , side-channel attacks 29 – 37 , SAT solver 38 – 45 , XSL attack 18 , 46 – 55 , XL attacks 56 – 60 .…”

Section: Introductionmentioning

confidence: 99%

Multilevel information fusion for cryptographic substitution box construction based on inevitable random noise in medical imaging

Khan

Saleem

Alshara

et al. 2021

Sci Rep

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Block cipher has been a standout amongst the most reliable option by which data security is accomplished. Block cipher strength against various attacks relies on substitution boxes. In literature, extensively algebraic structures, and chaotic systems-based techniques are available to design the cryptographic substitution boxes. Although, algebraic and chaotic systems-based approaches have favorable characteristics for the design of substitution boxes, but on the other side researchers have also pointed weaknesses in these approaches. First-time multilevel information fusion is introduced to construct the substitution boxes, having four layers; Multi Sources, Multi Features, Nonlinear Multi Features Whitening and Substitution Boxes Construction. Our proposed design does not hold the weakness of algebraic structures and chaotic systems because our novel s-box construction relies on the strength of true random numbers. In our proposed method true random numbers are generated from the inevitable random noise of medical imaging. The proposed design passes all the substitution box security evaluation criteria including Nonlinearity, Bit Independence Criterion (BIC), Strict Avalanche Criterion (SAC), Differential Approximation Probability (DP), Linear Approximation Probability (LP), and statistical tests, including resistance to Differential Attack, Correlation Analysis, 2D, 3D histogram analysis. The outcomes of the evaluation criteria validate that the proposed substitution boxes are effective for block ciphers; furthermore, the proposed substitution boxes attain better cryptographic strength as compared to very recent state-of-the-art techniques.

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Obtaining and Solving Systems of Equations in Key Variables Only for the Small Variants of AES

Cited by 8 publications

References 25 publications

Human Psychological Disorder towards Cryptography: True Random Number Generator from EEG of Schizophrenics and Its Application in Block Encryption’s Substitution Box

Human Psychological Disorder towards Cryptography: True Random Number Generator from EEG of Schizophrenics and Its Application in Block Encryption’s Substitution Box

S‐boxes representation and efficiency of algebraic attack

Multilevel information fusion for cryptographic substitution box construction based on inevitable random noise in medical imaging

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