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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > WORST CASE TO AVERAGE CASE REDUCTIONS:
Reports tagged with Worst case to average case reductions:
TR18-056 | 20th March 2018
Zvika Brakerski, Vadim Lyubashevsky, Vinod Vaikuntanathan, Daniel Wichs

Worst-Case Hardness for LPN and Cryptographic Hashing via Code Smoothing

We present a worst case decoding problem whose hardness reduces to that of solving the Learning Parity with Noise (LPN) problem, in some parameter regime. Prior to this work, no worst case hardness result was known for LPN (as opposed to syntactically similar problems such as Learning with Errors). The ... more >>>


TR20-095 | 24th June 2020
Mikito Nanashima

On Basing Auxiliary-Input Cryptography on NP-hardness via Nonadaptive Black-Box Reductions

Revisions: 1

A black-box (BB) reduction is a central proof technique in theoretical computer science. However, the limitations on BB reductions have been revealed for several decades, and the series of previous work gives strong evidence that we should avoid a nonadaptive BB reduction to base cryptography on NP-hardness (e.g., Akavia et ... more >>>


TR21-010 | 11th February 2021
Eric Allender, John Gouwar, Shuichi Hirahara, Caleb Robelle

Cryptographic Hardness under Projections for Time-Bounded Kolmogorov Complexity

Revisions: 1

A version of time-bounded Kolmogorov complexity, denoted KT, has received attention in the past several years, due to its close connection to circuit complexity and to the Minimum Circuit Size Problem MCSP. Essentially all results about the complexity of MCSP hold also for MKTP (the problem of computing the KT ... more >>>


TR22-007 | 14th January 2022
Halley Goldberg, Valentine Kabanets

A Simpler Proof of the Worst-Case to Average-Case Reduction for Polynomial Hierarchy via Symmetry of Information

We give a simplified proof of Hirahara's STOC'21 result showing that $DistPH \subseteq AvgP$ would imply $PH \subseteq DTIME[2^{O(n/\log n)}]$. The argument relies on a proof of the new result: Symmetry of Information for time-bounded Kolmogorov complexity under the assumption that $NP$ is easy on average, which is interesting in ... more >>>


TR22-020 | 18th February 2022
Vahid Reza Asadi, Alexander Golovnev, Tom Gur, Igor Shinkar

Worst-Case to Average-Case Reductions via Additive Combinatorics

We present a new framework for designing worst-case to average-case reductions. For a large class of problems, it provides an explicit transformation of algorithms running in time $T$ that are only correct on a small (subconstant) fraction of their inputs into algorithms running in time $\widetilde{O}(T)$ that are correct on ... more >>>




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