A Power Associative Loop Structure for the Construction of Non-Linear Components of Block Cipher

In the symmetric key cryptography, the purpose of the substitution box is to generate confusion and hence improve the security of the whole cryptosystem. For this reason, many algebraic substitution boxes are constructed depending upon the associative algebras of Galois fields. In this paper, the power associative loop is used for the construction of substitution boxes. This novel structure comprises excellent features which include, the inverse of zero element, non-associativity and fewer constraints as compared to the cyclic group and Galois field. In comparison to existing substitution boxes, the substitution boxes based upon power associative loop are comparatively easy and the above-mentioned properties offer the number of structures to construct highly nonlinear substitution boxes. To obtain the number of substitution boxes, we further applied the symmetric group of order 16 on the proposed substitution box. The evaluation of proposed boxes with different algebraic and statistical analyses like nonlinearity test, strict avalanche criterion, bit independence criterion, linear approximation probability and differential approximation probability indicate the strength of proposed substitution boxes. Majority logic criterion results depict that proposed substitution boxes have better cryptographic strength to apply in different techniques of secure communication.