Cryptographic Primitives with Quasigroup Transformations

The intention of this research is to justify deployment of quasigroups in cryptography,
especially with new quasigroup based cryptographic hash function NaSHA as a runner in
the First round of the ongoing NIST SHA-3 competition. We present new method for fast
generation of huge quasigroup operations, based on the so-called extended Feistel networks and
modification of the Sade’s diagonal method. We give new design of quasigroup based family
of cryptographic hash functions - NaSHA, which deploy the new method and with a novel
approach - different quasigroups for every application of component quasigroup transformations
in every iteration of the compression function and, much more, the used quasigroups are
functions of the processed message block.