Improved Local Leakage Resilience of Shamir Secret Sharing and Worst-Case Optimal Polynomial Intersection

arXiv:2610.12357 · quant-ph, cs.CR, cs.DM, cs.IT, math.IT · Submitted 2026-10-08 · Read on arXiv

quant-ph, cs.CR, cs.DM, cs.IT, math.IT

Submitted: 2026-10-08

Updated: 2026-10-08

Terminology

• Local Leakage Resilience — 19× in this paper
• Optimal Polynomial Intersection — 14× in this paper
• Consistency — 6× in this paper · explained in 3 episodes
• Decoded Quantum Interferometry — 5× in this paper
• Adam — 2× in this paper · explained in 2 episodes
• Combinatorial Optimization — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Decoded Quantum Interferometry (DQI) — 1× in this paper · explained in 2 episodes
• Query Complexity — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes

Sources

• Combinatorial Bounds for List Recovery via Discrete Brascamp--Lieb Inequalities
• OPI x Soft Decoders
• Discrepancy for Random Linear Codes
• Worst-Case Quantum Algorithm for Optimal Polynomial Intersection Beyond Decoded Quantum Interferometry
• A provable quantum advantage for approximate optimization via decoded quantum interferometry
• Tight inapproximability of max-LINSAT and implications for decoded quantum interferometry
• Verifiable Quantum Advantage via Optimized DQI Circuits
• True complexity and iterated Cauchy--Schwarz
• A nearly linear-time Decoded Quantum Interferometry algorithm for the Optimal Polynomial Intersection problem
• On Worst-Case Optimal Polynomial Intersection

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