Sample-Preserving Search-to-Decision Reduction for Noisy Linear Equations over Large Moduli
Researchers give a sample-preserving search-to-decision reduction for noisy linear equations that stays polynomial for exponential moduli.
The paper gives a sample-preserving search-to-decision reduction for Noisy Linear Equations, a generalization of LWE, LWR, and LPN. Its complexity is polynomial in the secret dimension n, sample count m, log q, and the ratio q/σ. For prime moduli, LWE and LWR reductions run in poly(n) time even when q is exponentially large, provided the noise-to-modulus ratio is non-negligible. For composite q, the reduction returns a list containing a small multiple of the solution, avoiding prior costs that scaled with σ or q's largest prime factor.
- Sample-preserving search-to-decision reduction for noisy linear equations.
- Complexity is polynomial in n, m, log q, and q/σ.
- LWE and LWR reductions stay poly(n) for exponential prime moduli.
- Composite moduli yield a list containing a small multiple of the secret.
From the original article
1 min read at arxiv.orgThe Noisy Linear Equations problem involves finding the solution to a random linear system over a finite field given noisy evaluations. This is a generalisation of various learning problems widely used in cryptography, including Learning with Errors (LWE), Learning with Rounding (LWR), and Learning Parity with Noise (LPN).
By Andrej Bogdanov · arxiv.org
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