In this paper we propose a definition and construction of a new family of
one-way candidate functions RNβ:QNβQN, where Q={0,1,...,sβ1}
is an alphabet with s elements. Special instances of these functions can have
the additional property to be permutations (i.e. one-way permutations). These
one-way functions have the property that for achieving the security level of
2n computations in order to invert them, only n bits of input are needed.
The construction is based on quasigroup string transformations. Since
quasigroups in general do not have algebraic properties such as associativity,
commutativity, neutral elements, inverting these functions seems to require
exponentially many readings from the lookup table that defines them (a Latin
Square) in order to check the satisfiability for the initial conditions, thus
making them natural candidates for one-way functions.Comment: Submitetd to conferenc