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

Efficient sharing of many secrets

Carlo Blundo, Alfredo De Santis, Ugo Vaccaro

Lecture notes in computer scienceJan 1, 199369 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

Keeping Secrets Secret

Ivars Peterson

Science NewsOct 17, 19810 citations

Computing on quantum shared secrets

Yingkai Ouyang, Si-Hui Tan, Liming Zhao +1 more

A ( $k,n$ )-threshold secret-sharing scheme allows for a string to be split into $n$ shares in such a way that any subset of at least $k$ shares suffices to recover the secret string, but such that any subset of at most $k\ensuremath{-}1$ shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation securely on quantum shared secrets. We introduce a ( $n,n$ )-quantum secret sharing scheme together with a set of algorithms that allow quantum circuits to be evaluated securely on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the algorithm.A ($k,n$)-threshold secret-sharing scheme allows for a string to be split into $n$ shares in such a way that any subset of at least $k$ shares suffices to recover the secret string, but such that any subset of at most $k\ensuremath{-}1$ shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation securely on quantum shared secrets. We introduce a ($n,n$)-quantum secret sharing scheme together with a set of algorithms that allow quantum circuits to be evaluated securely on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the algorithm.

arXiv:1702.03689Physical Review ANov 27, 201719 citations

Sharing Multiple Secrets: Models, Schemes and Analysis

Barbara Masucci

Designs Codes and CryptographyFeb 15, 200623 citations

A (

k,n

)-threshold secret-sharing scheme allows for a string to be split into

n

shares in such a way that any subset of at least

k

shares suffices to recover the secret string, but such that any subset of at most $k\ensuremath{-}1$ shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation securely on quantum shared secrets. We introduce a (

n,n

)-quantum secret sharing scheme together with a set of algorithms that allow quantum circuits to be evaluated securely on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the algorithm.