Abstract
We present a candidate counterexample to the easy cylinders conjecture, which was recently suggested by Manindra Agrawal and Osamu Watanabe (see ECCC, TR09-019). Loosely speaking, the conjecture asserts that any 1-1 function in \(\mathcal{P}\)poly can be decomposed into “cylinders” of sub-exponential size that can each be inverted by some polynomial-size circuit. Although all popular one-way functions have such easy (to invert) cylinders, we suggest a possible counterexample. Our suggestion builds on the candidate one-way function based on expander graphs (see ECCC, TR00-090), and essentially consists of iterating this function polynomially many times.
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References
Applebaum, B., Ishai, Y., Kushilevitz, E.: Cryptography in NC0. SICOMP 36(4), 845–888 (2006)
Agrawal, M., Watanabe, O.: One-Way Functions and the Isomorphism Conjecture. ECCC, TR09-019 (2009)
Goldreich, O.: Candidate One-Way Functions Based on Expander Graphs. In: Goldreich, O., et al.: Studies in Complexity and Cryptography. LNCS, vol. 6650, pp. 76–87. Springer, Heidelberg (2011)
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Goldreich, O. (2011). A Candidate Counterexample to the Easy Cylinders Conjecture. In: Goldreich, O. (eds) Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science, vol 6650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22670-0_16
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DOI: https://doi.org/10.1007/978-3-642-22670-0_16
Publisher Name: Springer, Berlin, Heidelberg
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