How to construct random functions
Journal of the ACM (JACM)
Journal of Computer and System Sciences
Pseudorandom generators in propositional proof complexity
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
SIAM Journal on Computing
Goldreich's One-Way Function Candidate and Myopic Backtracking Algorithms
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
On the Security of Goldreich's One-Way Function
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Public-key cryptography from different assumptions
Proceedings of the forty-second ACM symposium on Theory of computing
A candidate counterexample to the easy cylinders conjecture
Studies in complexity and cryptography
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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.