Two infinite classes of cryptographic hash functions

We offer two new definitions of two infinite classes of strongly collision free hash functions that we gave a name “Edon”–C and “Edon”– R. Beside the fact that “Edon” are infinite classes of hash functions, “Edon” hash functions have other “good” properties such as possibility to have variable length of output, and also their strongly collision free property can be mathematically and experimentally proved. The whole concept is based on the theory of quasigroups, and the cryptographic properties of string processing with quasigroups.