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.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:2302.14448IEICE Transactions on Fundamentals of Electronics Communications and Computer SciencesNov 23, 20234 citations

Quantum secret sharing

김상겸

Jan 1, 20000 citations

Advance Sharing of Quantum Shares for Classical Secrets

Rina Miyajima, Ryutaroh Matsumoto

Secret sharing schemes for classical secrets can be classified into classical secret sharing schemes and quantum secret sharing schemes. Classical secret sharing has been known to be able to distribute some shares before a given secret. On the other hand, quantum mechanics extends the capabilities of secret sharing beyond those of classical secret sharing. We propose quantum secret sharing with the capabilities in designing of access structures more flexibly and realizing higher efficiency beyond those of classical secret sharing, that can distribute some shares before a given secret.Secret sharing schemes for classical secrets can be classified into classical secret sharing schemes and quantum secret sharing schemes. Classical secret sharing has been known to be able to distribute some shares before a given secret. On the other hand, quantum mechanics extends the capabilities of secret sharing beyond those of classical secret sharing. We propose quantum secret sharing with the capabilities in designing of access structures more flexibly and realizing higher efficiency beyond those of classical secret sharing, that can distribute some shares before a given secret.

arXiv:2208.01847IEEE AccessJan 1, 20224 citations

Quantum Secret Sharing with Classical and Quantum Shares

Hua Sun

In quantum secret sharing, a quantum secret state is mapped to multiple shares such that shares from qualified sets can recover the secret state and shares from other forbidden sets reveal nothing about the secret state; we study the setting where there are both classical shares and quantum shares. We show that the quantum secret sharing problem with both classical and quantum shares is feasible if and only if any two qualified sets have some quantum share in common. Next, for threshold quantum secret sharing where there are $N_1$ classical shares, $N_2$ quantum shares and qualified sets consist of any $K_1$ (or more) classical shares and any $K_2 > N_2/2$ (or more) quantum shares, we show that to share $1$ qubit secret, each classical share needs to be at least $2$ bits and each quantum share needs to be at least $1$ qubit. Finally, we characterize the minimum share sizes for quantum secret sharing with at most $2$ classical shares and at most $2$ quantum shares. The converse proofs rely on quantum information inequalities and the achievable schemes use classical secret sharing, (encrypted) quantum secret sharing with only quantum shares, superdense coding, treating quantum digits as classical digits, and their various combinations.In quantum secret sharing, a quantum secret state is mapped to multiple shares such that shares from qualified sets can recover the secret state and shares from other forbidden sets reveal nothing about the secret state; we study the setting where there are both classical shares and quantum shares. We show that the quantum secret sharing problem with both classical and quantum shares is feasible if and only if any two qualified sets have some quantum share in common. Next, for threshold quantum secret sharing where there are $N_1$ classical shares, $N_2$ quantum shares and qualified sets consist of any $K_1$ (or more) classical shares and any $K_2 > N_2/2$ (or more) quantum shares, we show that to share $1$ qubit secret, each classical share needs to be at least $2$ bits and each quantum share needs to be at least $1$ qubit. Finally, we characterize the minimum share sizes for quantum secret sharing with at most $2$ classical shares and at most $2$ quantum shares. The converse proofs rely on quantum information inequalities and the achievable schemes use classical secret sharing, (encrypted) quantum secret sharing with only quantum shares, superdense coding, treating quantum digits as classical digits, and their various combinations.

arXiv:2507.17364Jul 23, 20250 citations

Sharing secrets using quantum physics

Zhonghua Ma

Mar 6, 20230 citations

N_1

classical shares,

N_2

quantum shares and qualified sets consist of any

K_1

(or more) classical shares and any

K_2 > N_2/2

(or more) quantum shares, we show that to share

1

qubit secret, each classical share needs to be at least

2

bits and each quantum share needs to be at least

1

qubit. Finally, we characterize the minimum share sizes for quantum secret sharing with at most

2

classical shares and at most

2

quantum shares. The converse proofs rely on quantum information inequalities and the achievable schemes use classical secret sharing, (encrypted) quantum secret sharing with only quantum shares, superdense coding, treating quantum digits as classical digits, and their various combinations.