A Quantum Evolving Secret Sharing Scheme
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A Quantum Evolving Secret Sharing Scheme Shion Samadder Chaudhury1 Received: 24 July 2020 / Accepted: 23 October 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract An evolving secret sharing scheme is supposed to accommodate unbounded number (potentially infinite) of new participants over time and the dealer should not know the set of participants in advance. In this paper we initiate the study of quantum evolving schemes to share a quantum secret and show how to construct such a scheme where the qualified subsets (the sets which can reconstruct the secret) of participants are of increasing size as the number of participants increases with time. Share is given to new participants without modifying shares of old participants. While quantum secret sharing schemes which can accommodate new participants over time have been constructed before, a quantum scheme which can handle an unbounded and unspecified number of participants has not been considered so far. We also discuss the resilience of our scheme against a bounded number of quantum queries by an adversary/eavesdropper. This is achieved by using special functions for which lower bounds on their quantum query complexity is known. Keywords Quantum evolving secret sharing · Resilient quantum secret sharing · Quantum query complexity · Quantum error-correcting codes
1 Introduction In a (k, n) threshold secret sharing scheme (TSSS) [7, 33] a secret is shared among n participants and any k or more of them are able to reconstruct the secret, while subsets of participants containing less that k participants have no information about the secret. The subsets which can (cannot) recover the secret are called qualified (forbidden) sets. Quantum versions of such schemes called quantum threshold secret sharing (QTSS) schemes where a secret (quantum or classical) is shared using quantum states have been extensively studied
Shion Samadder Chaudhury
[email protected] 1
Applied Statistics Unit, Indian Statistical Institute, Kolkata, India
International Journal of Theoretical Physics
[5, 14, 16, 20, 24, 26, 34, 35]. The purpose of quantum secret sharing is twofold : 1. protecting classical information, 2. protecting quantum information. As noted by the authors in [31] sharing the quantum state is more difficult than sharing the classical information. So the quantum secret sharing schemes that share the quantum state are much fewer than the ones that share the classical information. Some variants of secret sharing schemes allow to add or delete participants, to renew the shares, and to modify the conditions for accessing the secret. In the literature classical variants of these schemes are known by names such as dynamic, proactive, online secret sharing schemes etc. Quantum versions of these schemes were studied in [15, 19, 25, 30] and many more. Such constructions have certain limitations. For example, the dealer needs to know the number of new participants before-hand and the dealer also needs to know the set of qualified participa
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