Enhancing Algebraic Complexity and Randomness in Smallpresent-[2] through Key Schedule Algorithm Modification

This research modifies the Key Scheduling Algorithm (KSA) of the Smallpresent-[2] block cipher to enhance the algebraic complexity and randomness of round keys and ciphertext. The modification introduces a Key Register Obfuscation Function, dividing the key register into five interacting blocks and incorporating additional S-Boxes to boost non-linearity. Evaluations-including algebraic complexity analysis, NIST statistical randomness tests, Strict Avalanche Criterion (SAC), and Bit Independence Criterion (BIC)-demonstrate that the modified KSA significantly increases algebraic complexity, with round keys reaching up to 21 polynomial degrees and approximately 175 million unknown variables by round 3. The modified KSA also shows improved performance in randomness and diffusion tests from round 6 onward while maintaining execution efficiency, making it suitable for resource-constrained devices and enhancing the security of the Smallpresent-[2] cipher in lightweight cryptography applications.