No Escape from the Quadratic Barrier: Adaptive Attacks on Linear $\ell_2$ Sketches
Linear sketches estimate properties of high-dimensional inputs from a fixed low-dimensional projection. At constant accuracy, randomized Euclidean-norm sketches, notably the Johnson-Lindenstrauss transform, support exponentially many nonadaptive queries in sketch dimension $k$. For adaptive black-box queries, known privacy-based defenses guarantee $\widetildeΩ(k^2)$ and it remained open whether stronger guarantees were possible. Prior attacks used more queries, restricted the responder, or provided weaker failure guarantees. We show that the quadratic guarantee is optimal up to logarithmic factors, even with a computationally unbounded responder that knows the matrix, attack algorithm, hi...
| Authors | Edith Cohen, Uri Stemmer |
|---|---|
| Primary category | cs.DS |
| Published | 18 October 2026 |
| Last updated at source | 18 October 2026 |
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