Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1702.00942 · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Quantum Optimal Multiple Assignment Scheme for Realizing General Access Structure of Secret Sharing

Ryutaroh Matsumoto

Published Jan 1, 2017• 3 citations
arXivHTMLPDF

Abstract

The multiple assignment scheme is to assign one or more shares to single participant so that any kind of access structure can be realized by classical secret sharing schemes. We propose its quantum version including ramp secret sharing schemes. Then we propose an integer optimization approach to minimize the average share size.
DOI
10.1587/transfun.e100.a.726

Related papers

Advance Sharing of Quantum Shares for Quantum Secrets

Mamoru Shibata, Ryutaroh Matsumoto

Secret sharing is a cryptographic scheme to encode a secret to multiple shares being distributed to participants, so that only qualified sets of participants can restore the original secret from their shares. When we encode a secret by a secret sharing scheme and distribute shares, sometimes not all participants are accessible, and it is desirable to distribute shares to those participants before a secret information is determined. Secret sharing schemes for classical secrets have been known to be able to distribute some shares before a given secret. Lie et al. found a ((2, 3))-threshold secret sharing for quantum secrets can distribute some shares before a given secret. However, it is unknown whether distributing some shares before a given secret is possible with other access structures of secret sharing for quantum secrets. We propose a quantum secret sharing scheme for quantum secrets that can distribute some shares before a given secret with other access structures.

arXiv:2302.14448•IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Nov 23, 2023•4 citations

Ideal and perfect multi-secret sharing schemes whose access structure are Q 3

Lv yingli, Xiaojun Xu, Zhang Xiao-feng +1 more

The characterization of access structure is one of the main open problems in secret sharing schemes. We are particularly interested in determining which Q 3 access structures can be realized and the requirement should be achieved even in the presence of an adversary who is able to corrupt some players in an ideal secret sharing scheme. The problems are studied in our paper. Above all, we present a concrete scheme that can meet all above requirements. In our scheme, it is not only a dynamic multi-secret and multi-use sharing protocol, but participants from access structure can recover the secret using their shares, while the same number of participants from adversary structure can't recover the secret using their shares, which is different from general access structure schemes. Moreover, in the whole dynamic process, the coefficients of polynomial and private secret shares always stay the same. Therefore, it enjoys high practical value.

•Aug 1, 2012•0 citations

Quantum Access Structure and Secret Sharing

Chen‐Ming Bai, Zhihui Li, Yongming Li

In this paper we define a kind of decomposition for a quantum access structure. We propose a conception of minimal maximal quantum access structure and obtain a sufficient and necessary condition for minimal maximal quantum access structure, which shows the relationship between the number of minimal authorized sets and that of the players. Moreover, we investigate the construction of efficient quantum secret schemes by using these techniques, a decomposition and minimal maximal quantum access structure. A major advantage of these techniques is that it allows us to construct a method to realize a general quantum access structure. For these quantum access structures, we present two quantum secret schemes via the idea of concatenation or a decomposition of a quantum access structure. As a consequence, the application of these techniques allow us to save more quantum shares and reduce more cost than the existing scheme.

arXiv:1701.01951•Jan 8, 2017•0 citations

Exploring Quantum Supremacy in Access Structures of Secret Sharing by Coding Theory

Ryutaroh Matsumoto

We consider secret sharing schemes with a classical secret and quantum shares. One example of such schemes was recently reported whose access structure cannot be realized by any secret sharing schemes with classical shares. In this paper, we report further quantum secret sharing schemes whose access structures cannot be realized by any classical secret sharing schemes.

arXiv:1803.10392•International Symposium on Information Theory and its Applications•Oct 1, 2018•1 citation

Upper and lower bounds for secret sharing schemes with general access structures

Sofia Barbetta

Secret sharing schemes are a fundamental cryptographic tool for securely distributing sensitive information among multiple parties according to a specified access structure. For a given access policy, several schemes with different levels of efficiency may exist. One of the main parameters in this analysis is the share size and a central goal is to minimize it. This thesis studies the complexity of secret sharing schemes by focusing on lower and upper bounds on the share size for arbitrary and explicit access structures. The main objective is to collect the most relevant results in the literature, ranging from early lower bounds due to Karnin et al. and Csirmaz and upper-bound of Liu and Vaikuntanathan to recent advances that have significantly improved known bounds. Despite this progress, a significant gap between lower and upper bounds remains, leaving the determination of the optimal share size an open problem.

•Jan 27, 2026•0 citations

On quantum evolving schemes

Shion Samadder Chaudhury

A quantum secret sharing scheme is a method to share a quantum secret among participants in such a way that only certain specified subsets of the set of participants can combine to recover the secret. A quantum evolving secret sharing scheme is a recently introduced variant of secret sharing schemes where the sets of participants is not fixed and an unbounded and unspecified number of participants arrive one by one with time. The number of participants can be potentially infinite and and a quantum secret is shared and protected among the participants. The existing construction has some major drawbacks such as 1) the exponential quantum memory requirement and 2) the very high dimensions of the shares which makes the scheme difficult to implement. In this paper we overcome these drawbacks by constructing a scheme which uses quantum memory linear in the number of participants and significantly improves on the dimensions of the shares of the participants. This construction uses quantum secret redistribution and trap codes. The construction is flexible and can be modified to different types of access structures(subsets of participants which can recover the secret). Certain ramp properties can also be incorporated in the scheme.

Quantum Information and Computation•Apr 1, 2022•1 citation
Secret sharing is a cryptographic scheme to encode a secret to multiple shares being distributed to participants, so that only qualified sets of participants can restore the original secret from their shares. When we encode a secret by a secret sharing scheme and distribute shares, sometimes not all participants are accessible, and it is desirable to distribute shares to those participants before a secret information is determined. Secret sharing schemes for classical secrets have been known to be able to distribute some shares before a given secret. Lie et al. found a ((2, 3))-threshold secret sharing for quantum secrets can distribute some shares before a given secret. However, it is unknown whether distributing some shares before a given secret is possible with other access structures of secret sharing for quantum secrets. We propose a quantum secret sharing scheme for quantum secrets that can distribute some shares before a given secret with other access structures.
The characterization of access structure is one of the main open problems in secret sharing schemes. We are particularly interested in determining which Q 3 access structures can be realized and the requirement should be achieved even in the presence of an adversary who is able to corrupt some players in an ideal secret sharing scheme. The problems are studied in our paper. Above all, we present a concrete scheme that can meet all above requirements. In our scheme, it is not only a dynamic multi-secret and multi-use sharing protocol, but participants from access structure can recover the secret using their shares, while the same number of participants from adversary structure can't recover the secret using their shares, which is different from general access structure schemes. Moreover, in the whole dynamic process, the coefficients of polynomial and private secret shares always stay the same. Therefore, it enjoys high practical value.
In this paper we define a kind of decomposition for a quantum access structure. We propose a conception of minimal maximal quantum access structure and obtain a sufficient and necessary condition for minimal maximal quantum access structure, which shows the relationship between the number of minimal authorized sets and that of the players. Moreover, we investigate the construction of efficient quantum secret schemes by using these techniques, a decomposition and minimal maximal quantum access structure. A major advantage of these techniques is that it allows us to construct a method to realize a general quantum access structure. For these quantum access structures, we present two quantum secret schemes via the idea of concatenation or a decomposition of a quantum access structure. As a consequence, the application of these techniques allow us to save more quantum shares and reduce more cost than the existing scheme.
Secret sharing schemes are a fundamental cryptographic tool for securely distributing sensitive information among multiple parties according to a specified access structure. For a given access policy, several schemes with different levels of efficiency may exist. One of the main parameters in this analysis is the share size and a central goal is to minimize it. This thesis studies the complexity of secret sharing schemes by focusing on lower and upper bounds on the share size for arbitrary and explicit access structures. The main objective is to collect the most relevant results in the literature, ranging from early lower bounds due to Karnin et al. and Csirmaz and upper-bound of Liu and Vaikuntanathan to recent advances that have significantly improved known bounds. Despite this progress, a significant gap between lower and upper bounds remains, leaving the determination of the optimal share size an open problem.
A quantum secret sharing scheme is a method to share a quantum secret among participants in such a way that only certain specified subsets of the set of participants can combine to recover the secret. A quantum evolving secret sharing scheme is a recently introduced variant of secret sharing schemes where the sets of participants is not fixed and an unbounded and unspecified number of participants arrive one by one with time. The number of participants can be potentially infinite and and a quantum secret is shared and protected among the participants. The existing construction has some major drawbacks such as 1) the exponential quantum memory requirement and 2) the very high dimensions of the shares which makes the scheme difficult to implement. In this paper we overcome these drawbacks by constructing a scheme which uses quantum memory linear in the number of participants and significantly improves on the dimensions of the shares of the participants. This construction uses quantum secret redistribution and trap codes. The construction is flexible and can be modified to different types of access structures(subsets of participants which can recover the secret). Certain ramp properties can also be incorporated in the scheme.