A candidate counterexample to the easy cylinders conjecture

Authors:
Oded Goldreich
Affiliations:
Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Israel
Venue:
Studies in complexity and cryptography
Year:
2011

Citing 3
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Foundations of Cryptography: Basic Tools

Foundations of Cryptography: Basic Tools
Cryptography in $NC^0$

SIAM Journal on Computing
Candidate one-way functions based on expander graphs

Studies in complexity and cryptography

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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 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.