Joint data and key distribution of simple, multiple, and multidimensional linear cryptanalysis test statistic and its impact to data complexity

Blondeau, Céline; Nyberg, Kaisa

doi:10.1007/s10623-016-0268-6

Cited by 36 publications

(92 citation statements)

References 24 publications

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“…p of the key we observed in this paper has been considered, and more advanced statistical models have been developed. The variance due to random key was first integrated in the wrong key model of one-dimensional linear cryptanalysis [8], then to the model of the cipher [21] and finally for both [6] considering also explicitly the case of sampling without replacement. Since 2012, the hypothesis testing model has been adopted in many works on statistical cryptanalysis to determine distinguishing complexity [7] and data complexity for key recovery.…”

Section: Later Developmentsmentioning

confidence: 99%

Multidimensional Linear Cryptanalysis

2018

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Linear cryptanalysis introduced by Matsui is a statistical attack which exploits a binary linear relation between plaintext, ciphertext and key, either in Algorithm 1 for recovering one bit of information of the secret key of a block cipher, or in Algorithm 2 for ranking candidate values for a part of the key. The statistical model is based on the expected and observed bias of a single binary value. Multiple linear approximations have been used with the goal to make the linear attack more efficient. More bits of information of the key can potentially be recovered possibly using less data. But then also more elaborated statistical models are needed to capture the joint behaviour of several not necessarily independent binary variables. Also more options are available for generalising the statistics of a single variable to several variables. The multidimensional extension of linear cryptanalysis to be introduced in this paper considers using multiple linear approximations that form a linear subspace. Different extensions of Algorithm 1 and Algorithm 2 will be presented and studied. The methods will be based on known statistical tools such as goodness-of-fit test and log-likelihood ratio. The efficiency of the different methods will be measured and compared in theory and experiments using the concept of advantage introduced by Selçuk. The block cipher Serpent with a reduced number of rounds will be used as test bed. The multidimensional linear cryptanalysis will also be compared with previous methods that use biasedness of multiple linear approximations. It will be shown in the simulations that the multidimensional method is potentially more powerful. Its main theoretical advantage is that the statistical model can be given without the assumption about statistical independence of the linear approximations.

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Section: Later Developmentsmentioning

confidence: 99%

Multidimensional Linear Cryptanalysis

2018

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“…Later in [22,[30][31][32][33], more practical links between integral and zero-correlation linear distinguishers, impossible differential and zero-correlation linear distinguisher, truncated differential and multidimensional linear properties were proposed, which could significantly facilitate the task of evaluating security of block ciphers against various cryptanalytic tools. Recently, efforts have been made to provide more accurate estimates of data complexity of simple, multiple, and multidimensional linear cryptanalysis [34], or to improve the accuracy of estimated success probability of linear key-recovery attacks [35].…”

Section: Introductionmentioning

confidence: 99%

New insights on linear cryptanalysis

Liu

Han

Wang

et al. 2019

Sci. China Inf. Sci.

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Linear cryptanalysis of NUSH block cipher Science in China Series F-Information Sciences 45, 59 (2002); Evolutionary cryptography against multidimensional linear cryptanalysis SCIENCE CHINA Information Sciences 54, 2565 (2011); Probability method for cryptanalysis of general multivariate modular linear equation Science in China Series F-Information Sciences 52, 1792 (2009); Improved linear (hull) cryptanalysis of round-reduced versions of SIMON SCIENCE CHINA Information Sciences 60, 039101 (2017);

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“…Since its invention in the early 1990s, many variations and extensions have been considered. A statistical model to estimate the data complexity of linear attacks was introduced in [2]. In this paper, we focus on linear cryptanalysis of round-reduced block ciphers: Fantomas, Robin, and iSCREAM.…”

Section: Introductionmentioning

confidence: 99%

Cryptanalysis of Round-Reduced Fantomas, Robin and iSCREAM

et al. 2019

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In this work, we focus on LS-design ciphers Fantomas, Robin, and iSCREAM. LS-designs are a family of bitslice ciphers aimed at efficient masked implementations against side-channel analysis. We have analyzed Fantomas and Robin with a technique that previously has not been applied to both algorithms or linear cryptanalysis. The idea behind linear cryptanalysis is to build a linear characteristic that describes the relation between plaintext and ciphertext bits. Such a relationship should hold with probability 0.5 (bias is zero) for a secure cipher. Therefore, we try to find a linear characteristic between plaintext and ciphertext where bias is not equal to zero. This non-random behavior of cipher could be converted to some key-recovery attack. For Fantomas and Robin, we find 5 and 7-round linear characteristics. Using these characteristics, we attack both the ciphers with reduced rounds and recover the key for the same number of rounds. We also apply linear cryptanalysis to the famous CAESAR candidate iSCREAM and the closely related LS-design Robin. For iScream, we apply linear cryptanalysis to the round-reduced cipher and find a 7-round best linear characteristics. Based on those linear characteristics we extend the path in the related-key scenario for a higher number of rounds.

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Joint data and key distribution of simple, multiple, and multidimensional linear cryptanalysis test statistic and its impact to data complexity

Cited by 36 publications

References 24 publications

Multidimensional Linear Cryptanalysis

Multidimensional Linear Cryptanalysis

New insights on linear cryptanalysis

Cryptanalysis of Round-Reduced Fantomas, Robin and iSCREAM

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