Dynamic key scheduling algorithm for block ciphers using quasigroup string transformation

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(s). 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 on the secret key. 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 “Isotophism”, which literally means Different quasigroups that has the same order of elements but different arrangements can be generated from the existing one. This research proposed a Dynamic Key Scheduling Algorithm (KSA) using isotope of a quasigroup as the dynamic substitution table. A method of generating isotope from a non-associative quasigroup using one permutation with full inheritance is achieved. The generic quasigroup string transformation has been analyzed and it is found to be vulnerable to ciphertext only attack which eventually led to the proposal of a new quasigroup string transformation in this research to assess its strength as it has never been analyzed nor properly implemented before. Based on the dynamic shapeless quasigroup and the proposed new string transformation, a Dynamic Key Scheduling Algorithm (DKSA) is developed. 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 has been validated using the randomness test proposed and recommended by NIST, avalanche test and has achieved remarkable result of 94%, brute force and correlation assessment test with -0.000449 correlations. It was fully implemented in a modified Rijndael block cipher to validate it performance and it has produced a remarkable result of 3.35332 entropy

Quasigroup String Transformations and Hash Function Design

In this paper we propose two new types of compression functions, based on quasigroup string transformations. The first type uses known quasigroup string transformations, defined elsewhere, by changing alternately the transformation direction, going forward and backward through the string. Security of this design depends of the chosen quasigroup string transformation, the order of the quasigroup and the properties satisfied by the quasigroup operations. We illustrate how this type of compression function is applied in the design of the cryptographic hash function NaSHA. The second type of compression function uses new generic quasigroup string transformation, which combine two orthogonal quasigroup operations into a single one. This, in fact, is deployment of the concept of multipermutation for perfect generation of confusion and diffusion. One implementation of this transformation is by extended Feistel network F_{A,B,C} which has at least two orthogonal mates as orthomorphisms: its inverse F_{A,B,C}^{−1} and its square F_{A,B,C}^2

Quasigroup String Transformations and Hash Function Design

In this paper we propose two new types of compression functions, based on quasigroup string transformations. The first type uses known quasigroup string transformations, defined elsewhere, by changing alternately the transformation direction, going forward and backward through the string. Security of this design depends of the chosen quasigroup string transformation, the order of the quasigroup and the properties satisfied by the quasigroup operations. We illustrate how this type of compression function is applied in the design of the cryptographic hash function NaSHA. The second type of compression function uses new generic quasigroup string transformation, which combine two orthogonal quasigroup operations into a single one. This, in fact, is deployment of the concept of multipermutation for perfect generation of confusion and diffusion. One implementation of this transformation is by extended Feistel network F_{A,B,C} which has at least two orthogonal mates as orthomorphisms: its inverse F_{A,B,C}^{−1} and its square F_{A,B,C}^2