Unified Approach to Secret Sharing and Symmetric Private Information Retrieval with Colluding Servers in Quantum Systems
arXiv:2205.14622 · doi:10.1109/TIT.2023.3282940
Abstract
This paper unifiedly addresses two kinds of key quantum secure tasks, i.e., quantum versions of secret sharing (SS) and symmetric private information retrieval (SPIR) by using multi-target monotone span program (MMSP), which characterizes the classical linear protocols of SS and SPIR. SS has two quantum extensions; One is the classical-quantum (CQ) setting, in which the secret to be sent is classical information and the shares are quantum systems. The other is the quantum-quantum (QQ) setting, in which the secret to be sent is a quantum state and the shares are quantum systems. The relation between these quantum protocols and MMSP has not been studied sufficiently. We newly introduce the third setting, i.e., the entanglement-assisted (EA) setting, which is defined by modifying the CQ setting with allowing prior entanglement between the dealer and the end-user who recovers the secret by collecting the shares. Showing that the linear version of SS with the EA setting is directly linked to MMSP, we characterize linear quantum versions of SS with the CQ ad QQ settings via MMSP. Further, we introduce the EA setting of SPIR, which is shown to link to MMSP. In addition, we discuss the quantum version of maximum distance separable codes.
References in corpus (26)
- Quantum secret sharing
- Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
- How to share a quantum secret
- On the Theory of Quantum Secret Sharing
- Graph States for Quantum Secret Sharing
- Codes for the Quantum Erasure Channel
- Quantum secret sharing with qudit graph states
- Quantum Secret Sharing Schemes and Reversibility of Quantum Operations
- Quantum Codes of Maximal Distance and Highly Entangled Subspaces
- Non-Threshold Quantum Secret Sharing Schemes in the Graph State Formalism
- Private Information Retrieval from MDS Coded Databases with Colluding Servers under Several Variant Models
- Matroids and Quantum Secret Sharing Schemes
- On the equivalence between sharing quantum and classical secrets, and error correction
- Quantum secret sharing for general access structures
- Information Flow in Secret Sharing Protocols
- Secure Network Code for Adaptive and Active Attacks with No-Randomness in Intermediate Nodes
- Provably-secure symmetric private information retrieval with quantum cryptography
- Computation-aided classical-quantum multiple access to boost network communication speeds
- Capacity of Quantum Private Information Retrieval with Collusion of All But One of Servers
- On Weak Odd Domination and Graph-based Quantum Secret Sharing
- Quantum Strongly Secure Ramp Secret Sharing
- Privacy in Quantum Communication Complexity
- Classical Access Structures of Ramp Secret Sharing Based on Quantum Stabilizer Codes
- Coding Theoretic Construction of Quantum Ramp Secret Sharing
- Quantum Stabilizer Codes Can Realize Access Structures Impossible by Classical Secret Sharing
- Prior Entanglement Exponentially Improves One-Server Quantum Private Information Retrieval for Quantum Messages