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intelligence_src_e53adb99e40ae66258
observed · 2026-10-13 04:25:05 UTC
ePrint Report: Sample-Preserving Search-to-Decision Reduction for Noisy Linear Equations over Large Moduli Andrej Bogdanov, Kel Zin Tan, Prashant Nalini Vasudevan The 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). We present a new sample-preserving search-to-decision reduction for Noisy Linear Equations that has complexity $\mathrm{poly}(n,m,\log q, q/\sigma)$, where $n$ is the dimension of the secret, $m$ is the number of samples, $q$ is the modulus, and $\sigma$ is the magnitude of the noise (defined suitably for the kind of noise involved). In particular, this implies search-to-decision reductions for LWE and LWR that run in time $\mathrm{poly}(n)$ even if the modulus $q$ is exponentially large, as long as the noise-to-modulus ratio $\sigma/q$ is non-negligible. Our reduction works for prime moduli $q$. If $q$ is composite, it instea
Fingerprint: dbc15a84a38e259e2ae63e4c5ee53dea43efc8eba4e35fd2501a745502457077
intelligence_src_e53adb99e40ae66258
observed · 2026-10-12 16:25:03 UTC
available
Fingerprint: 366cb966e32414edc1db353849a1ee8d6b8462b83786e04001881ba6594765ad