Substitution boxes (S-boxes) are the fundamental mechanisms in symmetric key cryptosystems. These S-boxes guarantee that the cryptosystem is cryptographically secure and make them nonlinear. The S-boxes used in conventional and modern cryptography are mostly constructed over finite Galois field extensions of binary Field $$\mathbb {F}_{2}$$ . We have presented a novel construction scheme of S-boxes which is based on the elements of subgroups of multiplicative groups of units of the commutative finite chain rings of type $$\frac{\mathbb {F}_{2}[u]}{\langle u^{k}\rangle }$$ , where $$2\le k\le 8$$ . Majority logic criterion (MLC) is applied on the apprehended S-boxes owing to, checked their strength.