CryptoDB
Sample Efficient Search to Decision for kLIN
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| Conference: | CRYPTO 2025 |
| Abstract: | The $k$LIN problem concerns solving noisy systems of random sparse linear equations mod 2. It~gives rise to natural candidate hard CSP distributions and is a cornerstone of local cryptography. Recently, it was used in cryptographic constructions, under the name ``sparse LPN". For constant sparsity $k$ and inverse polynomial noise rate, both search and decision versions of $k$LIN are statistically possible and conjectured to be computationally hard for $n\ll m\ll n^{k/2}$, where $m$ is the number of $k$-sparse linear equations, and $n$ is the number of variables. We show an algorithm that given access to a distinguisher for $(k-1)$LIN with $m$ samples, solves search $k$LIN with roughly $O(nm)$ samples. Previously, it was only known how to reduce from search $k$LIN with $O(m^3)$ samples, yielding guarantees for decision $k$LIN only when $m \ll n^{k/6}$. The reduction succeeds even if the distinguisher has sub-constant advantage at a small additive cost in sample complexity. Our technique applies with some restrictions to Goldreich's function and $k$LIN with random coefficients over other finite fields. |
BibTeX
@inproceedings{crypto-2025-35653,
title={Sample Efficient Search to Decision for kLIN},
publisher={Springer-Verlag},
author={Andrej Bogdanov and Alon Rosen and Kel Zin Tan},
year=2025
}