A candidate counterexample to the easy cylinders conjecture

Oded Goldreich

doi:10.1007/978-3-642-22670-0_16

A candidate counterexample to the easy cylinders conjecture

Oded Goldreich

Department of Computer Science and Applied Mathematics

Weizmann Institute of Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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 &Pmathcal;/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.

Original language	English
Title of host publication	Studies in Complexity and Cryptography
Subtitle of host publication	Miscellanea on the Interplay between Randomness and Computation
Editors	Oded Goldreich
Chapter	16
Pages	136-140
Number of pages	5
DOIs	https://doi.org/10.1007/978-3-642-22670-0_16
State	Published - 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6650 LNCS

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

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10.1007/978-3-642-22670-0_16

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Goldreich, O. (2011). A candidate counterexample to the easy cylinders conjecture. In O. Goldreich (Ed.), Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation (pp. 136-140). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6650 LNCS). https://doi.org/10.1007/978-3-642-22670-0_16

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Goldreich, O 2011, A candidate counterexample to the easy cylinders conjecture. in O Goldreich (ed.), Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6650 LNCS, pp. 136-140. https://doi.org/10.1007/978-3-642-22670-0_16

A candidate counterexample to the easy cylinders conjecture. / Goldreich, Oded.
Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. ed. / Oded Goldreich. 2011. p. 136-140 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6650 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AB - 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 &Pmathcal;/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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Goldreich O. A candidate counterexample to the easy cylinders conjecture. In Goldreich O, editor, Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. 2011. p. 136-140. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-22670-0_16

A candidate counterexample to the easy cylinders conjecture

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