Recently, a class of quantum secret sharing schemes called communication efficient quantum threshold secret sharing schemes (CE-QTS) was introduced. These schemes reduced the quantum communication cost during secret recovery in quantum threshold secret sharing schemes. However, non-threshold schemes are known to have less storage cost compared to threshold schemes. This motivates us to extend the idea of communication efficiency to non-threshold schemes as well. In this paper, we introduce a general class of communication efficient quantum secret sharing schemes (CE-QSS) which include both threshold and non-threshold schemes. Specifically, we provide a framework for constructing CE-QSS schemes by concatenating a pair of CSS codes. The main component in this framework is a new class of Calderbank-Shor-Steane (CSS) codes called the extended CSS codes.Recently, a class of quantum secret sharing schemes called communication efficient quantum threshold secret sharing schemes (CE-QTS) was introduced. These schemes reduced the quantum communication cost during secret recovery in quantum threshold secret sharing schemes. However, non-threshold schemes are known to have less storage cost compared to threshold schemes. This motivates us to extend the idea of communication efficiency to non-threshold schemes as well. In this paper, we introduce a general class of communication efficient quantum secret sharing schemes (CE-QSS) which include both threshold and non-threshold schemes. Specifically, we provide a framework for constructing CE-QSS schemes by concatenating a pair of CSS codes. The main component in this framework is a new class of Calderbank-Shor-Steane (CSS) codes called the extended CSS codes.

arXiv:2211.06910International Symposium on Turbo Codes and Iterative Information ProcessingSep 4, 20234 citations

Theory of Communication Efficient Quantum Secret Sharing

Kaushik Senthoor, Pradeep Kiran Sarvepalli

A $((k,n))$ quantum threshold secret sharing (QTS) scheme is a quantum cryptographic protocol for sharing a quantum secret among $n$ parties such that the secret can be recovered by any $k$ or more parties while $k-1$ or fewer parties have no information about the secret. Despite extensive research on these schemes, there has been very little study on optimizing the quantum communication cost during recovery. Recently, we initiated the study of communication efficient quantum threshold secret sharing (CE-QTS) schemes. These schemes reduce the communication complexity in QTS schemes by accessing $d>k$ parties for recovery; here $d$ is fixed ahead of encoding the secret. In contrast to the standard QTS schemes which require $k$ qudits for recovering each qudit in the secret, these schemes have a lower communication cost of $\frac {d}{d-k+1}$ . In this paper, we further develop the theory of communication efficient quantum threshold schemes. Here, we propose universal CE-QTS schemes which reduce the communication cost for all $d>k$ simultaneously. We provide a framework based on ramp quantum secret sharing to construct CE-QTS and universal CE-QTS schemes. We give another construction for universal CE-QTS schemes based on Staircase codes. We derived a lower bound on communication complexity and show that our constructions are optimal. Finally, an information theoretic model is developed to analyse CE-QTS schemes and the lower bound on communication complexity is proved again using this model.A$((k,n))$quantum threshold secret sharing (QTS) scheme is a quantum cryptographic protocol for sharing a quantum secret among$n$parties such that the secret can be recovered by any$k$or more parties while$k-1$or fewer parties have no information about the secret. Despite extensive research on these schemes, there has been very little study on optimizing the quantum communication cost during recovery. Recently, we initiated the study of communication efficient quantum threshold secret sharing (CE-QTS) schemes. These schemes reduce the communication complexity in QTS schemes by accessing$d>k$parties for recovery; here$d$is fixed ahead of encoding the secret. In contrast to the standard QTS schemes which require$k$qudits for recovering each qudit in the secret, these schemes have a lower communication cost of$\frac {d}{d-k+1}$. In this paper, we further develop the theory of communication efficient quantum threshold schemes. Here, we propose universal CE-QTS schemes which reduce the communication cost for all$d>k$simultaneously. We provide a framework based on ramp quantum secret sharing to construct CE-QTS and universal CE-QTS schemes. We give another construction for universal CE-QTS schemes based on Staircase codes. We derived a lower bound on communication complexity and show that our constructions are optimal. Finally, an information theoretic model is developed to analyse CE-QTS schemes and the lower bound on communication complexity is proved again using this model.

arXiv:2101.12419IEEE Transactions on Information TheoryJan 7, 202240 citations

Threshold Quantum Secret Sharing of Secure Direct Communication

李宝奎, 杨宇光, Wen Qiao Yan

Chinese Physics LettersJan 1, 20091 citation

Quantum secret sharing with minimized quantum communication

Ben Fortescue, Gilad Gour

Bulletin of the American Physical SocietyMar 19, 20130 citations

Universal Communication Efficient Quantum Threshold Secret Sharing Schemes

Kaushik Senthoor, Pradeep Kiran Sarvepalli

Quantum secret sharing (QSS) is a cryptographic protocol in which a quantum secret is distributed among a number of parties where some subsets of the parties are able to recover the secret while some subsets are unable to recover the secret. In the standard ((k, n)) quantum threshold secret sharing scheme, any subset of k or more parties out of the total n parties can recover the secret while other subsets have no information about the secret. But recovery of the secret incurs a communication cost of at least k qudits for every qudit in the secret. Recently, a class of communication efficient QSS schemes were proposed which can improve this communication cost to $\frac{d}{{d - k + 1}}$ by contacting d ≥ k parties where d is fixed prior to the distribution of shares. In this paper, we propose a more general class of ((k, n)) quantum secret sharing schemes with low communication complexity. In these schemes the combiner can contact any d parties at the time of recovery where k ≤ d ≤ n. This is the first such class of universal communication efficient quantum threshold schemes.Quantum secret sharing (QSS) is a cryptographic protocol in which a quantum secret is distributed among a number of parties where some subsets of the parties are able to recover the secret while some subsets are unable to recover the secret. In the standard ((k, n)) quantum threshold secret sharing scheme, any subset of k or more parties out of the total n parties can recover the secret while other subsets have no information about the secret. But recovery of the secret incurs a communication cost of at least k qudits for every qudit in the secret. Recently, a class of communication efficient QSS schemes were proposed which can improve this communication cost to $\frac{d}{{d - k + 1}}$ by contacting d ≥ k parties where d is fixed prior to the distribution of shares. In this paper, we propose a more general class of ((k, n)) quantum secret sharing schemes with low communication complexity. In these schemes the combiner can contact any d parties at the time of recovery where k ≤ d ≤ n. This is the first such class of universal communication efficient quantum threshold schemes.

arXiv:2002.09229IEEE Information Theory Workshop (ITW)Apr 11, 20216 citations

((k,n))

quantum threshold secret sharing (QTS) scheme is a quantum cryptographic protocol for sharing a quantum secret among

n

parties such that the secret can be recovered by any

k

or more parties while

k-1

or fewer parties have no information about the secret. Despite extensive research on these schemes, there has been very little study on optimizing the quantum communication cost during recovery. Recently, we initiated the study of communication efficient quantum threshold secret sharing (CE-QTS) schemes. These schemes reduce the communication complexity in QTS schemes by accessing

d>k

parties for recovery; here

d

is fixed ahead of encoding the secret. In contrast to the standard QTS schemes which require

k

qudits for recovering each qudit in the secret, these schemes have a lower communication cost of

\frac {d}{d-k+1}

. In this paper, we further develop the theory of communication efficient quantum threshold schemes. Here, we propose universal CE-QTS schemes which reduce the communication cost for all

d>k

simultaneously. We provide a framework based on ramp quantum secret sharing to construct CE-QTS and universal CE-QTS schemes. We give another construction for universal CE-QTS schemes based on Staircase codes. We derived a lower bound on communication complexity and show that our constructions are optimal. Finally, an information theoretic model is developed to analyse CE-QTS schemes and the lower bound on communication complexity is proved again using this model.

\frac{d}{{d - k + 1}}

by contacting d ≥ k parties where d is fixed prior to the distribution of shares. In this paper, we propose a more general class of ((k, n)) quantum secret sharing schemes with low communication complexity. In these schemes the combiner can contact any d parties at the time of recovery where k ≤ d ≤ n. This is the first such class of universal communication efficient quantum threshold schemes.