Revision History for: Quantum Secret Sharing using GHZ States
- 2026-06-10 at 10:17 by Mina Doosti
implements Quantum Secret Sharing
Introduction
Quantum secret sharing (QSS) is a quantum protocol that grants unconditional security for communication. The scheme allows a secret holder Alice can split her secret into $n$ shares and send them to $ n$ others, when and only when $ k (\frac{n}{2}< k \le n)$ or more shares work together can recover the secret. Formally, we call the scheme $(k,n)$ secret sharing.Outline
((k,n)) threshold scheme
The simple case described above can be extended similarly to that done in CSS by Shamir [4] and Blakley [5] via a thresholding scheme. In the ((k,n)) threshold scheme (double parentheses denoting a quantum scheme), Alice splits her secret key (quantum state) into n shares such that any k≤n shares are required to extract the full information but k-1 or less shares cannot extract any information about Alice’s key.
The number of users needed to extract the secret is bounded by n/2 < k ≤ n. Consider for n ≥ 2k, if a ((k,n)) threshold scheme is applied to two disjoint sets of k in n, then two independent copies of Alice’s secret can be reconstructed. This of course would violate the no-cloning theorem and is why n must be less than 2k.
As long as a ((k,n)) threshold scheme exists, a ((k,n-1)) threshold scheme can be constructed by simply discarding one share. This method can be repeated until k=n.
Assumptions
[TBA]
Requirements
No content has been added to this section, yet!
Notation
No content has been added to this section, yet!
Properties
[TBA]
Technical Description
[TBA]
Experimental Implementations
”Experimental demonstration of quantum secret sharing” [3] was the first experimental demonstration of QSS in 2001.
Further Information
Quantum entanglement for secret sharing and secret splitting [2] is a similar scheme developed shortly after Hillery et al’s GHZ scheme, using Bell states instead of GHZ states.
References
1. Hillery, Mark, Vladimír Buifmmode checkzelse žfiek, and André Berthiaume. ‘Quantum Secret Sharing’. Phys. Rev. A 59 (March 1999): 1829–34. https://doi.org/10.1103/PhysRevA.59.1829.2. Karlsson, Anders, Masato Koashi, and Nobuyuki Imoto. ‘Quantum Entanglement for Secret Sharing and Secret Splitting’. Phys. Rev. A 59 (January 1999): 162–68. https://doi.org/10.1103/PhysRevA.59.162.3. Tittel, W., H. Zbinden, and N. Gisin. ‘Experimental Demonstration of Quantum Secret Sharing’. Phys. Rev. A 63 (March 2001): 042301. https://doi.org/10.1103/PhysRevA.63.042301.4. Shamir, Adi. ‘How to Share a Secret’. Commun. ACM 22, no. 11 (November 1979): 612–13. https://doi.org/10.1145/359168.359176.5. G. R. Blakley, “Safeguarding cryptographic keys,” in Managing Requirements Knowledge, International Workshop on, NEW YORK, 1979, pp. 313, doi: 10.1109/AFIPS.1979.98. https://doi.ieeecomputersociety.org/10.1109/AFIPS.1979.98 - 2026-06-07 at 23:10 by kimworrall
implements Quantum Secret Sharing
Introduction
Quantum secret sharing (QSS) is a quantum protocol that grants unconditional security for communication. The scheme allows a secret holder Alice can split her secret into $n$ shares and send them to $ n$ others, when and only when $ k (\\\frac{n}{2}< k \\\le n)$ or more shares work together can recover the secret. Formally, we call the scheme $(k,n)$ secret sharing.Outline
((k,n)) threshold scheme
The simple case described above can be extended similarly to that done in CSS by Shamir [4] and Blakley [5] via a thresholding scheme. In the ((k,n)) threshold scheme (double parentheses denoting a quantum scheme), Alice splits her secret key (quantum state) into n shares such that any k≤n shares are required to extract the full information but k-1 or less shares cannot extract any information about Alice’s key.
The number of users needed to extract the secret is bounded by n/2 < k ≤ n. Consider for n ≥ 2k, if a ((k,n)) threshold scheme is applied to two disjoint sets of k in n, then two independent copies of Alice’s secret can be reconstructed. This of course would violate the no-cloning theorem and is why n must be less than 2k.
As long as a ((k,n)) threshold scheme exists, a ((k,n-1)) threshold scheme can be constructed by simply discarding one share. This method can be repeated until k=n.
Assumptions
[TBA]
Requirements
No content has been added to this section, yet!
Notation
No content has been added to this section, yet!
Properties
[TBA]
Technical Description
[TBA]
Experimental Implementations
”Experimental demonstration of quantum secret sharing” [3] was the first experimental demonstration of QSS in 2001.
Further Information
Quantum entanglement for secret sharing and secret splitting [2] is a similar scheme developed shortly after Hillery et al’s GHZ scheme, using Bell states instead of GHZ states.
References
1. Hillery, Mark, Vladimír Buifmmode checkzelse žfiek, and André Berthiaume. ‘Quantum Secret Sharing’. Phys. Rev. A 59 (March 1999): 1829–34. https://doi.org/10.1103/PhysRevA.59.1829.2. Karlsson, Anders, Masato Koashi, and Nobuyuki Imoto. ‘Quantum Entanglement for Secret Sharing and Secret Splitting’. Phys. Rev. A 59 (January 1999): 162–68. https://doi.org/10.1103/PhysRevA.59.162.3. Tittel, W., H. Zbinden, and N. Gisin. ‘Experimental Demonstration of Quantum Secret Sharing’. Phys. Rev. A 63 (March 2001): 042301. https://doi.org/10.1103/PhysRevA.63.042301.4. Shamir, Adi. ‘How to Share a Secret’. Commun. ACM 22, no. 11 (November 1979): 612–13. https://doi.org/10.1145/359168.359176.5. G. R. Blakley, “Safeguarding cryptographic keys,” in Managing Requirements Knowledge, International Workshop on, NEW YORK, 1979, pp. 313, doi: 10.1109/AFIPS.1979.98. https://doi.ieeecomputersociety.org/10.1109/AFIPS.1979.98 - 2026-03-24 at 22:04 by kimworrall
implements Quantum Secret Sharing
Introduction
Quantum secret sharing (QSS) is a quantum protocol that grants unconditional security for communication. The scheme allows a secret holder Alice can split her secret into $n$ shares and send them to $ n$ others, when and only when $ k (\\\frac{n}{2}< k \\\le n)$ or more shares work together can recover the secret. Formally, we call the scheme $(k,n)$ secret sharing.Outline
((k,n)) threshold scheme
The simple case described above can be extended similarly to that done in CSS by Shamir [4] and Blakley [5] via a thresholding scheme. In the ((k,n)) threshold scheme (double parentheses denoting a quantum scheme), Alice splits her secret key (quantum state) into n shares such that any k≤n shares are required to extract the full information but k-1 or less shares cannot extract any information about Alice’s key.
The number of users needed to extract the secret is bounded by n/2 < k ≤ n. Consider for n ≥ 2k, if a ((k,n)) threshold scheme is applied to two disjoint sets of k in n, then two independent copies of Alice’s secret can be reconstructed. This of course would violate the no-cloning theorem and is why n must be less than 2k.
As long as a ((k,n)) threshold scheme exists, a ((k,n-1)) threshold scheme can be constructed by simply discarding one share. This method can be repeated until k=n.
Assumptions
[TBA]
Requirements
No content has been added to this section, yet!
Notation
No content has been added to this section, yet!
Properties
[TBA]
Technical Description
[TBA]
Experimental Implementations
“Experimental demonstration of quantum secret sharing” [3] was the first experimental demonstration of QSS in 2001.
Further Information
Quantum entanglement for secret sharing and secret splitting [2] is a similar scheme developed shortly after Hillery et al’s GHZ scheme, using Bell states instead of GHZ states.
References
1. Hillery, Mark, Vladimír Buifmmode checkzelse žfiek, and André Berthiaume. ‘Quantum Secret Sharing’. Phys. Rev. A 59 (March 1999): 1829–34. https://doi.org/10.1103/PhysRevA.59.1829.2. Karlsson, Anders, Masato Koashi, and Nobuyuki Imoto. ‘Quantum Entanglement for Secret Sharing and Secret Splitting’. Phys. Rev. A 59 (January 1999): 162–68. https://doi.org/10.1103/PhysRevA.59.162.3. Tittel, W., H. Zbinden, and N. Gisin. ‘Experimental Demonstration of Quantum Secret Sharing’. Phys. Rev. A 63 (March 2001): 042301. https://doi.org/10.1103/PhysRevA.63.042301.4. Shamir, Adi. ‘How to Share a Secret’. Commun. ACM 22, no. 11 (November 1979): 612–13. https://doi.org/10.1145/359168.359176.5. G. R. Blakley, “Safeguarding cryptographic keys,” in Managing Requirements Knowledge, International Workshop on, NEW YORK, 1979, pp. 313, doi: 10.1109/AFIPS.1979.98. https://doi.ieeecomputersociety.org/10.1109/AFIPS.1979.98 - 2026-02-26 at 08:32 by kimworrall
implements Quantum Secret Sharing
Introduction
[TBA]
Related Paper(s)
[TBA]
Outline
[TBA]
Assumptions
[TBA]
Requirements
No content has been added to this section, yet!
Notation
No content has been added to this section, yet!
Properties
[TBA]
Technical Description
[TBA]
Experimental Implementations
No content has been added to this section, yet!
Further Information
No content has been added to this section, yet!
References
[TBA]