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TR00-090 | 3rd December 2000 00:00
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#### Candidate One-Way Functions Based on Expander Graphs

**Abstract:**
We suggest a candidate one-way function using combinatorial

constructs such as expander graphs. These graphs are used to

determine a sequence of small overlapping subsets of input bits,

to which a hard-wired random predicate is applied.

Thus, the function is extremely easy to evaluate:

all that is needed is to take multiple projections of the

input bits, and to use these as entries to a look-up table.

It is feasible for the adversary to scan the look-up table,

but we believe it would be infeasible to find an input that fits a given

sequence of values obtained for these overlapping projections.

The conjectured difficulty of inverting the suggested function

does not seem to follow from any well-known assumption.

Instead, we propose the study of the complexity of inverting

this function as an interesting open problem,

with the hope that further research will provide evidence to our

belief that the inversion task is intractable.