Titanium S-Boxes: A New Family of 4-bit Optimal S-Boxes for Feistel-Based Lightweight Block Ciphers

Abstract

Substitution boxes (S-boxes) are the main nonlinear components in lightweight block ciphers (LBCs), including Feistel-based designs. Whereas existing S-boxes achieve optimal resistance to differential attacks (DAs), most remain vulnerable to boomerang (BAs) and algebraic (AAs) attacks, and often their assessment overlook cipher-specific features, such as the self-invertible structure of Feistel ciphers and the presence of a bit permutation layer. In this work, we introduce a family of 4-bit optimal S-boxes for Feistel-based LBCs (FLBCs), which we designate as Titanium S-boxes. These S-boxes are designed to attain optimal values for security properties related to DAs, BAs, AAs, and linear attacks. Their analysis incorporates cipher-specific features within a constrained exhaustive search approach, which reduces the search space by exploiting affine and permutation equivalence. Evaluation shows that Titanium S-boxes provide a higher security level than those used in FLBCs, such as WARP, SCENERY, TWINE, LBlock, and the ELSM S-box. Furthermore, for FLBCs with a bit permutation layer, Titanium S-boxes provide a competitive alternative for ciphers, such as SFN and Eight-Side Fortress. Even though Platinum, Serpent-type, and BOGI-applicable S-boxes are also viable options, Titanium S-boxes offer enhanced security against BAs, AAs, and DAs.