Computational Quantum Secret Sharing - Alper Cakan | TQC 2023
Channel: Squid: Schools for Quantum Information Development
Date: 2023-08-22

Alper Cakan 
Computational Quantum Secret Sharing 

https://arxiv.org/abs/2305.00356    
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security).  While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security.  We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of $n$-party access structures to $1.5^{n+o(n)}$, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in $\mathsf{P}$ and $\mathsf{NP}$.
July 25, 2023
--------
TQC 2023 | 24-28 July 2023, University of Aveiro, Portugal
http://tqc-conference.org

18th Conference on the  Theory of Quantum Computation, Communication and Cryptography.

TQC is a leading annual international conference for students and researchers working in the theoretical aspects of quantum information science. The scientific objective is to bring together the theoretical quantum information science community to present and discuss the latest advances in the field.


Organisation:
Squids - Schools for Quantum Information Development  
Universidade de Aveiro: Departamento de Matemática, CIDMA & Fábrica


Sponsors:
Phasecraft, UK
Google Quantum AI, USA
QuSoft, The Netherlands
Quantum for Life Centre, Denmark
Technology Innovation Institute, UAE
ML4Q, Germany
Dulwich Quantum