In this paper we present a comprehensive survey and developments of existing literature of non-associative rings and enumerate some of their various applications in different directions to date. These applications explain the voluminous work in different fields of non-associative rings and through which various algebraic structures in theoretical point of view could be developed.
In this manuscript, we put forward a standard based on fuzzy decision making criterion to examine the current substitution boxes and study their strengths and weaknesses in order to decide their appropriateness in image encryption applications. The proposed standard utilizes the results of correlation analysis, entropy analysis, contrast analysis, homogeneity analysis, energy analysis, and mean of absolute deviation analysis. These analyses are applied to well-known substitution boxes. The outcome of these analyses are additional observed and a fuzzy soft set decision making criterion is used to decide the suitability of an S-box to image encryption applications.
We prove the existence of nonassociative LA-ring and LA-field and discuss some of their special cases. We also give some computational information about them.
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