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.

Research on the Grading Theory of Thick and Thin Defects in the Electronic Testing for Raw Silk

2011 ◽  
Vol 175-176 ◽  
pp. 439-444 ◽  
Author(s):  
Jian Tao Niu ◽  
Qi Hu ◽  
Jian Mei Xu ◽  
Suo Zhuai Dong ◽  
Lun Bai
Keyword(s):  
Negative Binomial ◽  
Mean And Variance ◽  
The Mean ◽  
Spot Tests ◽  
The Difference ◽  
Grading Standards ◽  
The Right ◽  
Power Law Equation ◽  
The Relationship ◽  
Electronic Detector

Based on the sampling and grading theory of raw silk test, this paper studied the grading theory method of thick and thin defects of the raw silk in the electronic testing. By means of analyzing the data obtained from the raw silk electronic detector, the fact that the thick and thin defects of the raw silk appropriately take negative binomial distribution in the electronic testing has been confirmed. Under such circumstance, the distribution of the average of the sampling samples of the thick and thin defects was given, and fitting on the relationship between the mean and variance of the thick and thin defects were carried out by introducing Taylor’s power law equation, thus the right grading rate and probability of the difference between two spot tests about the thick and thin defects of the raw silk in the electronic testing was deduced. Moreover, the conclusion of the theoretical analysis was confirmed by simulation tests. The results might provide a basis for establishing the grading standards of the thick and thin defects in the electronic testing for raw silk.

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 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 Jack knifing for semivariogram validation

Bragantia ◽  
2010 ◽  
Vol 69 (suppl) ◽  
pp. 97-105 ◽  
Author(s):  
Sidney Rosa Vieira ◽  
José Ruy Porto de Carvalho ◽  
Antonio Paz González
Keyword(s):  
Correlation Coefficient ◽  
Square Root ◽  
Trend Surface ◽  
Strong Trend ◽  
Function Fitting ◽  
Mean And Variance ◽  
The Mean ◽  
The Difference ◽  
Distinct Field ◽  
The Ideal

The semivariogram function fitting is the most important aspect of geostatistics and because of this the model chosen must be validated. Jack knifing may be one the most efficient ways for this validation purpose. The objective of this study was to show the use of the jack knifing technique to validate geostatistical hypothesis and semivariogram models. For that purpose, topographical heights data obtained from six distinct field scales and sampling densities were analyzed. Because the topographical data showed very strong trend for all fields as it was verified by the absence of a sill in the experimental semivariograms, the trend was removed with a trend surface fitted by minimum square deviation. Semivariogram models were fitted with different techniques and the results of the jack knifing with them were compared. The jack knifing parameters analyzed were the intercept, slope and correlation coefficient between measured and estimated values, and the mean and variance of the errors calculated by the difference between measured and estimated values, divided by the square root of the estimation variances. The ideal numbers of neighbors used in each estimation was also studied using the jack knifing procedure. The jack knifing results were useful in the judgment of the adequate models fitted independent of the scale and sampling densities. It was concluded that the manual fitted semivariogram models produced better jack knifing parameters because the user has the freedom to choose a better fit in distinct regions of the semivariogram.

scholarly journals Fitness patterns and phenotypic plasticity in a spatially heterogeneous environment

1996 ◽  
Vol 68 (3) ◽  
pp. 241-248 ◽  
Author(s):  
Lev A. Zhivotovsky ◽  
Marcus W. Feldman ◽  
Aviv Bergman
Keyword(s):  
Environmental Heterogeneity ◽  
Genetic System ◽  
Quadratic Functions ◽  
Heterogeneous Environment ◽  
Mean And Variance ◽  
Haploid Population ◽  
The Mean ◽  
The Difference ◽  
Analytical Expressions ◽  
Special Case

SummaryWe analyse patterns of the means and variances of genotypic fitnesses across different niches in a randomly mating haploid population. The population inhabits a spatially heterogeneous environment where it is subject to mutation and weak multilocus additive selection, with different selection coefficients in different niches. Approximate analytical expressions are derived for the stationary mean and variance of genotypic fitnesses among the niches in terms of environmental and genetic parameters. As a special case, we analyse an environment described by a variable t, distributed among the niches with mean t* and variance D*, and quadratic decrease in correlation between environments as a function of the difference in values of t. If the niches have the same qualities, the mean and variance of genotypic fitnesses evolve to be quadratic functions of t that achieve their maximum and minimum, respectively, at t*. With unequal niche qualities, these are non-polynomial functions that attain their extrema at different, usually intermediate values of t, although the coefficient of variation of the genotypic fitnesses still attains its minimum near t*. The functions involve the total mutation rate, the contribution of the loci to genotypic fitnesses, and the frequency and quality distributions of the niches. Thus, for this relatively simple model the norms of reaction may be calculated in terms of the detailed properties of the environmental heterogeneity, and the genetic system.

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.

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