A projective general linear group based algorithm for the construction of substitution box for block ciphers

The substitution boxes are used in block ciphers with the purpose to induce confusion in data. The design of a substitution box determines the confusion ability of the cipher; therefore, many different types of boxes have been proposed by various authors in literature. In this paper, we present a novel method to design a new substitution box and compare its characteristics with some prevailing boxes used in cryptography. The algorithm proposed in this paper apply the action of projective linear group PGL(2, GF(28)) on Galois field GF(28). The new substitution box corresponds to a particular type of linear fractional transformation (35z + 15)/(9z + 5). In order to test the strength of the proposed substitution box, we apply non-linearity test, bit independence criterion, linear approximation probability method, differential approximation probability method, strict avalanche criterion, and majority logic criterion. This new technique to synthesize a substitution box offers a powerful algebraic complexity while keeping the software/hardware complexity within manageable parameters.