Quantum Leakage Resilience of Shamir Secret Sharing
Shamir secret sharing stays quantum-leakage resilient above a threshold rate near 0.73, unless entanglement is unbounded.
The paper analyzes unmodified Shamir secret sharing over prime fields when each party leaks one qubit from its share. Without preshared entanglement, the distinguishing advantage is 2 to the minus Omega(n) when the threshold rate t/n exceeds about 0.733 by a fixed margin. Security also holds for fixed-size entangled blocks and for a small linear fraction of devices entangled with the adversary when the threshold is high enough. A GHZ state shared by exactly t leakage devices makes even classical one-bit leakage insecure, since joint parity distinguishes a chosen secret pair with constant advantage.
- Quantum single-qubit leakage is secure above a threshold rate near 0.733.
- A small linear fraction of adversary-entangled devices can still be tolerated.
- A t-party GHZ state breaks classical one-bit leakage with constant advantage.
- The optimal entanglement support fraction above that rate remains open.
From the original article
1 min read at arxiv.orgWe initiate the study of quantum leakage resilience of unmodified Shamir secret sharing over prime fields. A well-studied leakage model for Shamir's secret sharing classically is single-bit local leakage from each share. We consider its quantum analogue where, for each party, a local leakage channel takes as input the party's share and outputs a leaked qubit.
By Rishabh Batra · arxiv.org
A short excerpt; the article and its images belong to the publisher. Summary, key facts and assessment above are AI-written from the article and can be wrong.