scholarly journals Linear Approximation Analysis: an improved technique for linear cryptanalysis of 4-bit Bijective Crypto S-Boxes

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Linear Approximation ◽  
Boolean Functions ◽  
Linear Cryptanalysis ◽  
Linear Relations ◽  
Linear Approximations ◽  
Input And Output ◽  
Approximation Analysis ◽  
Improved Technique

4-bit Linear Relations play an important role in Cryptanalysis of 4-bit Bijective S-Boxes. Count of existence of all 4-bit Linear Relations, for all of 16 input and output 4-bit bit patterns of 4-bit Bijective S-Boxes said as S-Boxes has been reported in Linear Cryptanalysis of 4-bit S-Boxes. In this paper a brief review of this cryptanalytic method for 4-bit S-Boxes has been introduced in a very lucid and conceptual manner. A new Analysis to search for the existing Linear Approximations among the input Boolean Functions (BFs) and output BFs of a particular 4-bit S-Box has also been introduced in this paper. The search is limited to find the existing Linear Relations or Approximations in the contrary to count the number existence among all 16 4-bit input and output bit patterns for all possible linear approximations.

scholarly journals Linear Approximation Analysis: an improved technique for linear cryptanalysis of 4-bit Bijective Crypto S-Boxes

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Linear Approximation ◽  
Boolean Functions ◽  
Linear Cryptanalysis ◽  
Linear Relations ◽  
Linear Approximations ◽  
Input And Output ◽  
Approximation Analysis ◽  
Improved Technique

4-bit Linear Relations play an important role in Cryptanalysis of 4-bit Bijective S-Boxes. Count of existence of all 4-bit Linear Relations, for all of 16 input and output 4-bit bit patterns of 4-bit Bijective S-Boxes said as S-Boxes has been reported in Linear Cryptanalysis of 4-bit S-Boxes. In this paper a brief review of this cryptanalytic method for 4-bit S-Boxes has been introduced in a very lucid and conceptual manner. A new Analysis to search for the existing Linear Approximations among the input Boolean Functions (BFs) and output BFs of a particular 4-bit S-Box has also been introduced in this paper. The search is limited to find the existing Linear Relations or Approximations in the contrary to count the number existence among all 16 4-bit input and output bit patterns for all possible linear approximations.

scholarly journals A review of existing 4-bit crypto S-box cryptanalysis techniques and two new techniques with 4-bit Boolean functions for cryptanalysis of 4-bit crypto S-boxes

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Finite Differences ◽  
Boolean Functions ◽  
Major Part ◽  
Linear Cryptanalysis ◽  
New Techniques ◽  
Linear Relations ◽  
Analysis Techniques ◽  
Linear Approximations ◽  
Input And Output ◽  
Substitution Boxes

4-bit Linear Relations play an important role in Cryptanalysis of 4-bit Bijective Crypto S-boxes. 4-bit finite differences also a major part of cryptanalysis of 4-bit substitution boxes. Count of existence of all 4-bit linear relations, for all of 16 input and 16 output 4-bit bit patterns of 4-bit bijective crypto S-boxes said as S-boxes has been reported in Linear Cryptanalysis of 4-bit S-boxes. Count of existing finite differences from each element of output S-boxes to distant output S-boxes have been noted in Differential Cryptanalysis of S-boxes. In this paper a brief review of these cryptanalytic methods for 4-bit S-boxes has been introduced in a very lucid and conceptual manner. Two new Analysis Techniques, one to search for the existing Linear Approximations among the input Boolean Functions (BFs) and output BFs of a particular 4-bit S-Box has also been introduced in this paper. The search is limited to find the existing linear relations or approximations in the contrary to count the number existent linear relations among all 16 4-bit input and output bit patterns within all possible linear approximations. Another is to find number of balanced 4-bit BFs in difference output S-boxes. Better the number of Balanced BFs, Better the security.

scholarly journals A review of existing 4-bit crypto S-box cryptanalysis techniques and two new techniques with 4-bit Boolean functions for cryptanalysis of 4-bit crypto S-boxes

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Finite Differences ◽  
Boolean Functions ◽  
Major Part ◽  
Linear Cryptanalysis ◽  
New Techniques ◽  
Linear Relations ◽  
Analysis Techniques ◽  
Linear Approximations ◽  
Input And Output ◽  
Substitution Boxes

4-bit Linear Relations play an important role in Cryptanalysis of 4-bit Bijective Crypto S-boxes. 4-bit finite differences also a major part of cryptanalysis of 4-bit substitution boxes. Count of existence of all 4-bit linear relations, for all of 16 input and 16 output 4-bit bit patterns of 4-bit bijective crypto S-boxes said as S-boxes has been reported in Linear Cryptanalysis of 4-bit S-boxes. Count of existing finite differences from each element of output S-boxes to distant output S-boxes have been noted in Differential Cryptanalysis of S-boxes. In this paper a brief review of these cryptanalytic methods for 4-bit S-boxes has been introduced in a very lucid and conceptual manner. Two new Analysis Techniques, one to search for the existing Linear Approximations among the input Boolean Functions (BFs) and output BFs of a particular 4-bit S-Box has also been introduced in this paper. The search is limited to find the existing linear relations or approximations in the contrary to count the number existent linear relations among all 16 4-bit input and output bit patterns within all possible linear approximations. Another is to find number of balanced 4-bit BFs in difference output S-boxes. Better the number of Balanced BFs, Better the security.

scholarly journals Partly-Pseudo-Linear Cryptanalysis of Reduced-Round Speck

Cryptography ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
Sarah A. Alzakari ◽  
Poorvi L. Vora
Keyword(s):  
Linear Approximation ◽  
Block Ciphers ◽  
Linear Cryptanalysis ◽  
Key Recovery ◽  
Linear Approximations ◽  
Key Recovery Attacks

We apply McKay’s pseudo-linear approximation of addition modular 2n to lightweight ARX block ciphers with large words, specifically the Speck family. We demonstrate that a pseudo-linear approximation can be combined with a linear approximation using the meet-in-the-middle attack technique to recover several key bits. Thus we illustrate improvements to Speck linear distinguishers based solely on Cho–Pieprzyk approximations by combining them with pseudo-linear approximations, and propose key recovery attacks.

scholarly journals New Linear Cryptanalysis of Chinese Commercial Block Cipher Standard SM4

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yu Liu ◽  
Huicong Liang ◽  
Wei Wang ◽  
Meiqin Wang
Keyword(s):  
Wireless Communication ◽  
Linear Approximation ◽  
Block Cipher ◽  
Linear Cryptanalysis ◽  
Key Recovery ◽  
Linear Approximations ◽  
Partial Linear ◽  
Key Recovery Attack ◽  
Better Than

SM4 is a Chinese commercial block cipher standard used for wireless communication in China. In this paper, we use the partial linear approximation table of S-box to search for three rounds of iterative linear approximations of SM4, based on which the linear approximation for 20-round SM4 has been constructed. However, the best previous identified linear approximation only covers 19 rounds. At the same time, a linear approximation for 19-round SM4 is obtained, which is better than the known results. Furthermore, we show the key recovery attack on 24-round SM4 which is the best attack according to the number of rounds.

scholarly journals Statistical Model of Correlation Difference and Related-Key Linear Cryptanalysis

2021 ◽  
pp. 124-137
Author(s):  
Kaisa Nyberg
Keyword(s):  
Boolean Functions ◽  
Multinomial Distribution ◽  
Linear Cryptanalysis ◽  
Multivariate Normal ◽  
Linear Approximations ◽  
Multidimensional Linear Approximation ◽  
Multivariate Normal Approximation ◽  
Mean And Variance ◽  
The Mean ◽  
The Difference

The goal of this work is to propose a related-key model for linear cryptanalysis. We start by giving the mean and variance of the difference of sampled correlations of two Boolean functions when using the same sample of inputs to compute both correlations. This result is further extended to determine the mean and variance of the difference of correlations of a pair of Boolean functions taken over a random data sample of fixed size and over a random pair of Boolean functions. We use the properties of the multinomial distribution to achieve these results without independence assumptions. Using multivariate normal approximation of the multinomial distribution we obtain that the distribution of the difference of related-key correlations is approximately normal. This result is then applied to existing related-key cryptanalyses. We obtain more accurate right-key and wrong-key distributions and remove artificial assumptions about independence of sampled correlations. We extend this study to using multiple linear approximations and propose a Χ2-type statistic, which is proven to be Χ2 distributed if the linear approximations are independent. We further examine this statistic for multidimensional linear approximation and discuss why removing the assumption about independence of linear approximations does not work in the related-key setting the same way as in the single-key setting.

Tools in Analyzing Linear Approximation for Boolean Functions Related to FLIP

2018 ◽  
pp. 282-303 ◽  
Author(s):  
Subhamoy Maitra ◽  
Bimal Mandal ◽  
Thor Martinsen ◽  
Dibyendu Roy ◽  
Pantelimon Stănică
Keyword(s):  
Linear Approximation ◽  
Boolean Functions

scholarly journals Crypto-Archaeology: unearthing design methodology of DES s-boxes

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Design Methodology ◽  
Block Cipher ◽  
Block Ciphers ◽  
Public Domain ◽  
Differential Cryptanalysis ◽  
Linear Cryptanalysis ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

US defence sponsored the DES program in 1974 and released it in 1977. It remained as a well-known and well accepted block cipher until 1998. Thirty-two 4-bit DES S-Boxes are grouped in eight each with four and are put in public domain without any mention of their design methodology. S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers. In this paper, while looking into the design methodology of DES S-Boxes, we find that S-Boxes have 128 balanced and non-linear Boolean Functions, of which 102 used once, while 13 used twice and 92 of 102 satisfy the Boolean Function-level Strict Avalanche Criterion. All the S-Boxes satisfy the Bit Independence Criterion. Their Differential Cryptanalysis exhibits better results than the Linear Cryptanalysis. However, no S-Boxes satisfy the S-Box-level SAC analyses. It seems that the designer emphasized satisfaction of Boolean-Function-level SAC and S-Box-level BIC and DC, not the S-Box-level LC and SAC.

scholarly journals Multidimensional linear cryptanalysis with key difference invariant bias for block ciphers

Cybersecurity ◽  
2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Wenqin Cao ◽  
Wentao Zhang
Keyword(s):  
Time Complexity ◽  
Block Ciphers ◽  
Linear Cryptanalysis ◽  
Compression Technique ◽  
Key Recovery ◽  
Linear Approximations ◽  
Theoretical Advantage ◽  
Multidimensional Linear ◽  
Multidimensional Linear Cryptanalysis ◽  
Key Recovery Attacks

AbstractFor block ciphers, Bogdanov et al. found that there are some linear approximations satisfying that their biases are deterministically invariant under key difference. This property is called key difference invariant bias. Based on this property, Bogdanov et al. proposed a related-key statistical distinguisher and turned it into key-recovery attacks on LBlock and TWINE-128. In this paper, we propose a new related-key model by combining multidimensional linear cryptanalysis with key difference invariant bias. The main theoretical advantage is that our new model does not depend on statistical independence of linear approximations. We demonstrate our cryptanalysis technique by performing key recovery attacks on LBlock and TWINE-128. By using the relations of the involved round keys to reduce the number of guessed subkey bits. Moreover, the partial-compression technique is used to reduce the time complexity. We can recover the master key of LBlock up to 25 rounds with about 260.4 distinct known plaintexts, 278.85 time complexity and 261 bytes of memory requirements. Our attack can recover the master key of TWINE-128 up to 28 rounds with about 261.5 distinct known plaintexts, 2126.15 time complexity and 261 bytes of memory requirements. The results are the currently best ones on cryptanalysis of LBlock and TWINE-128.

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