The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers

Substitution boxes are the only nonlinear component of the symmetric key cryptography and play a key role in the cryptosystem. In block ciphers, the S-boxes create confusion and add valuable strength. The majority of the substitution boxes algorithms focus on bijective Boolean functions and primitive irreducible polynomial that generates the Galois field. For binary field F2, there are exactly 16 primitive irreducible polynomials of degree 8 and it prompts us to construct 16 Galois field extensions of order 256. Conventionally, construction of affine power affine S-box is based on Galois field of order 256, depending on a single degree 8 primitive irreducible polynomial over ℤ2. In this manuscript, we study affine power affine S-boxes for all the 16 distinct degree 8 primitive irreducible polynomials over ℤ2 to propose 16 different 8×8 substitution boxes. To perform this idea, we introduce 16 affine power affine transformations and, for fixed parameters, we obtained 16 distinct S-boxes. Here, we thoroughly study S-boxes with all possible primitive irreducible polynomials and their algebraic properties. All of these boxes are evaluated with the help of nonlinearity test, strict avalanche criterion, bit independent criterion, and linear and differential approximation probability analyses to measure the algebraic and statistical strength of the proposed substitution boxes. Majority logic criterion results indicate that the proposed substitution boxes are well suited for the techniques of secure communication.

S-box Construction Based on Linear Fractional Transformation and Permutation Function

Substitution boxes (S-box) with strong and secure cryptographic properties are widely used for providing the key property of nonlinearity in block ciphers. This is critical to be resistant to a standard attack including linear and differential cryptanalysis. The ability to create a cryptographically strong S-box depends on its construction technique. This work aims to design and develop a cryptographically strong 8 × 8 S-box for block ciphers. In this work, the construction of the S-box is based on the linear fractional transformation and permutation function. Three steps involved in producing the S-box. In step one, an irreducible polynomial of degree eight is chosen, and all roots of the primitive irreducible polynomial are calculated. In step two, algebraic properties of linear fractional transformation are applied in Galois Field GF (28). Finally, the produced matrix is permuted to add randomness to the S-box. The strength of the S-box is measured by calculating its potency to create confusion. To analyze the security properties of the S-box, some well-known and commonly used algebraic attacks are used. The proposed S-box is analyzed by nonlinearity test, algebraic degree, differential uniformity, and strict avalanche criterion which are the avalanche effect test, completeness test, and strong S-box test. S-box analysis is done before and after the application of the permutation function and the analysis result shows that the S-box with permutation function has reached the optimal properties as a secure S-box.

Evaluation of Stiffness Degradation Curves from in Situ Tests in Various Soil Types

Increasingly complex design systems require an individual approach when determining the necessary design parameters. As soils are characterized by strong strain-dependent nonlinearity, test methods used to characterize the subsoil should be carefully selected, in terms of their “sensitivity” as well as suitability for the analyzed type of problem. When direct measurements are not available, while design calculation models require specific parameters, indirect parameter estimation may be used. This approach requires calibration and validation of empirical correlations, based on well documented database of tests and case studies. One of the parameters often used, when analyzing soil-structure interaction problems, is the shear stiffness of the soil and its strain-dependent degradation. The aim of the article is to present the procedure for description and evaluation of soil stiffness based on field tests (CPTU, DMT and SDMT) and a large number of reference curves obtained from laboratory tests (TRX) for selected soil types. On the basis of the given algorithm, it is possible to obtain a stiffness module G0 value at any level of deformation, based on in-situ tests.

Examining the presence of nonlinear relationship between natural gas consumption and economic growth in nigeria

This paper examines the Presence of Nonlinear Relationship between Natural Gas Consumption and Economic Growth in Nigeria from 1981 to 2015. The Ramsey Reset test,Incremental F-test, and Wald test have been employed to test for non-linearity in the relationship between natural gas consumption and economic growth in Nigeria. The nonlinearity test results revealed that the relationship is nonlinear. However, the results are suggestive of the fact that linear models might not be the appropriate statistical tools for estimating the relationship between natural gas consumption and economic growth in Nigeria. Therefore, the paper recommends that the Nigeria’s policymakers consider taking into cognizance nonlinear modeling techniques as alternative tools for modeling, estimating and forecasting the relationship between natural gas consumption and economic growth in the country.

KAJIAN PEMODELAN DERET WAKTU NONLINIER THRESHOLD AUTOREGRESSIVE (TAR)

Nonlinear time series are time series that are not stable due to a sudden jump. Nonlinear time series often found in financial data. Threshold Autoregressive (TAR) modeling is a time series modeling with a segmented autoregressive (AR)’s model such that among different regimes may have different AR model. This research studied how to obtain the Ordinary Least Square (OLS) estimator for TAR model and examine signification the OLS’s estimator by using t test. This research also studied the other stages of TAR modeling, which are nonlinearity test using Tsay test, TAR model identification by using arranged AR approach and Akaike’s Information Criterion (AIC), and diagnostic test by examining the white noise properties and normality test on the residuals. As an illustration, the TAR modeling was applied on weekly data of rupiah exchange rate against US dollar for period October 4th 2004 to November 7th 2011. The result show that the best TAR model for the data is TAR with threshold value .