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