A Key Scheduling Algorithm Based on Dynamic Quasigroup String Transformation and All-Or-Nothing Key Derivation Function

Abstract

Cryptographic ciphers depend on how quickly the key affects the output of the ciphers (ciphertext). Keys are traditionally generated from small size input (Seed) to a bigger size random key. Key scheduling algorithm (KSA) is the mechanism that generates and schedules all sub-keys for each round of encryption. Researches have suggested that sub-keys should be generated separately to avoid related-key attack. Similarly, the key space should be disproportionately large to resist any attack meant for secret keys. To archive that, some algorithms adopt the use of matrixes such as quasigroup, Hybrid cubes and substitution box (S-box) to generate the encryption keys. Quasigroup has other algebraic property called “Isotopism”, which literally means Different quasigroups that has the same order of elements but different arrangements. This paper proposed a Dynamic Key Scheduling Algorithm (KSA) using Isotope of a quasigroup as the dynamic substitution table. The proposed algorithm is a modification and upgrade to Allor-nothing Key Derivation Function (AKDF). To minimize the complexity of the algorithm, a method of generating Isotope from a non-associative quasigroup using one permutation is achieved. To validate the findings, non-associativity of the generated isotopes has been tested and the generated isotopes appeared to be non-associative. Furthermore, the proposed KSA algorithm will be validated using the Randomness test proposed and recommended by NIST, Avalanche and Correlation Assessment test.