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**2005/352**

**Title:**

Candidate One-Way Functions and One-Way Permutations Based on Quasigroup String Transformations

**Authors:**
Danilo Gligoroski

**Abstract:**

In this paper we propose a definition and construction of a new

family of one-way candidate functions {\cal R}_N:Q^N \rightarrow
Q^N, where Q=\{0,1,\ldots,s-1\} 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 2^n 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.

**ePrint:**
https://eprint.iacr.org/2005/352

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