arXiv subjects

Geoffroy Couteau

Publications and source records attributed to Geoffroy Couteau.

3 recordsLinked to original sources

arXiv2026

Hardness Self-Amplification in Linear Algebra and Fine-Grained Cryptography

We study the possibility of basing fine-grained cryptography on the hardness of fundamental problems in linear algebra. Our main technical contribution is a hardness self-amplification method based on random low-rank updates: we show how to turn an algorithm that solves an inverse-polynomial fraction of random linear systems into a solver which succeeds for every right-hand side of almost every matrix. Our reduction increases the runtime only linearly in the inverse of the original success probability. In particular, this yields fine-grained one-way functions from the almost worst-case hardness of linear systems over large enough fields. Using the same approach, we also obtain tighter worst-case to average-case reductions for matrix multiplication and online matrix-vector multiplication, as well as variants of our reductions that recover exact solutions from approximate algorithms, whose expected coordinate agreement is only $1/q+\varepsilon$, with inverse-quadratic dependence on $\varepsilon$ up to logarithmic factors, over every finite field. Finally, we also use it to connect the existence of fine-grained key agreement to the problem of computing the rank of a matrix: over a suitable sequence of growing characteristic-two fields, the almost-everywhere average-case hardness of rank computation (for any of a large class of distributions) implies infinitely-often fine-grained key agreement.

cs.CC↗

arXiv2026

Interactive Proofs of Proximity for Model Evaluation

We study interactive proofs of proximity (IPPs) for model evaluation, where a resource-limited verifier interacts with an untrusted prover, typically the model owner, to certify statistical properties of a model under an unknown input distribution. Our formulation separates sampling the input distribution from querying the model and evaluating its output; distinguishes real audit data (black-box sampling) from generated data (chosen-randomness, or gray-box, access to the sampler); and allows the prover and verifier to use different evaluators. We focus on doubly-sublinear IPPs, where both the verifier and honest prover use sublinear resources, and on (weighted) Hamming weight properties. For ordinary Hamming weight, we give a tolerant doubly-sublinear IPP. For completeness and soundness radii $\varepsilon_c<\varepsilon_f$ and gap $g=\varepsilon_f-\varepsilon_c$, a logarithmic-round instantiation uses $\widetilde{O}(1/g)$ verifier queries and $O(1/g^2)$ honest-prover queries, improving the cubic dependence of Amir, Goldreich, and Rothblum (ITCS 2025). We prove matching query lower bounds up to polylogarithmic factors. For distribution-weighted Hamming weight, black-box sampling requires $Θ(1/g^2)$ verifier samples but only $\widetilde{O}(1/g)$ evaluations; the quadratic sample complexity is necessary in the interior regime. With chosen-randomness access, the problem reduces to ordinary Hamming weight, yielding $\widetilde{O}(1/g)$ calls and evaluations. If the parties' evaluators disagree arbitrarily on a $ρ$-fraction of the distribution and by at most $γ$ elsewhere, our protocols remain doubly sublinear whenever $g>2κ$, where $κ=ρ+(1-ρ)γ$. Applications include auditing accuracy, group fairness, calibration, harmlessness, usefulness, and average-case robustness.

cs.CC↗

arXiv2023

Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding

Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle $\textit{et al.}$ (CCS 2018, Crypto 2019) showed how pseudorandom correlation generators (PCG) can be used to generate large amounts of useful forms of correlated (pseudo)randomness, using minimal interactions followed solely by local computations, yielding silent secure two-party computation protocols (protocols where the preprocessing phase requires almost no communication). An additional property called programmability allows to extend this to build N-party protocols. However, known constructions for programmable PCG's can only produce OLE's over large fields, and use rather new splittable Ring-LPN assumption. In this work, we overcome both limitations. To this end, we introduce the quasi-abelian syndrome decoding problem (QA-SD), a family of assumptions which generalises the well-established quasi-cyclic syndrome decoding assumption. Building upon QA-SD, we construct new programmable PCG's for OLE's over any field $\mathbb{F}_q$ with $q>2$. Our analysis also sheds light on the security of the ring-LPN assumption used in Boyle $\textit{et al.}$ (Crypto 2020). Using our new PCG's, we obtain the first efficient N-party silent secure computation protocols for computing general arithmetic circuit over $\mathbb{F}_q$ for any $q>2$.

cs.CR↗