Malaysian Journal of Mathematical Sciences, December 2022, Vol. 16, No. 4
A New Design of Substitution Box with Ideal Strict Avalanche Criterion
Mohd Esa, N. F., Abdul-Latip, S. F., and Abu, N. A.
Corresponding Email: shekhfaisal@utem.edu.my
Received date: 23 March 2022
Accepted date: 4 September 2022
Abstract:
The use of S-boxes (substitution boxes) to provide nonlinear properties is known to be
a common way to design a block cipher. These nonlinear properties are necessary to
ensure the security of a block cipher. This manuscript proposes a design construction
of a new S-box using affine transformation via cellular automata as a permutation
matrix. We incorporate this cellular-automaton permutation matrix into the AES Sbox
structure and test various irreducible polynomials. Nonlinearity, bijection, bit
independence criterion, strict avalanche effect, linear approximation probability, and
differential uniformity are the standard performance requirements used to evaluate the S-boxes that arise. Using this method, we are able to determine an irreducible polynomial that enables the construction of a new S-box design that can achieve an ideal strict avalanche criterion (SAC), which will subsequently provide efficiency in the design of block ciphers.
Keywords: substitution-box; irreducible polynomial; cellular automata; strict avalanche criterion
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