Abstract
In this paper, we consider to use the quantum stabilizer codes as secret sharing schemes for classical secrets. We give necessary and sufficient conditions for qualified and forbidden sets in terms of quantum stabilizers. Then, we give a Gilbert–Varshamov-type sufficient condition for existence of secret sharing schemes with given parameters, and by using that sufficient condition, we show that roughly 19% of participants can be made forbidden independently of the size of classical secret, in particular when an n-bit classical secret is shared among n participants having 1-qubit share each. We also consider how much information is obtained by an intermediate set and express that amount of information in terms of quantum stabilizers. All the results are stated in terms of linear spaces over finite fields associated with the quantum stabilizers.
Highlights
Secret sharing is a scheme to share a secret among multiple participants so that only qualified sets of participants can reconstruct the secret, while forbidden sets have noAn extended abstract [28] of this manuscript appeared in https://www.lebesgue.fr/content/sem2019WCC-programthe Proceedings of the Eleventh International Workshop on Coding and Cryptography (WCC 2019), Saint-Jacut-de-la-Mer, France, March 31–April 5, 2019
Page 3 of 16 9 for existence of secret sharing schemes with given parameters, and by using that sufficient condition, we show that roughly 19% of participants can be made forbidden independently of the size of classical secret, which cannot be realized by classical shares, in Sect
We considered construction of secret sharing schemes for classical secrets by quantum stabilizer codes and clarified their access structures, that is, qualified and forbidden sets, in terms of underlying quantum stabilizers
Summary
Secret sharing is a scheme to share a secret among multiple participants so that only qualified sets of participants can reconstruct the secret, while forbidden sets have no. An extended abstract [28] of this manuscript appeared in https://www.lebesgue.fr/content/sem2019WCC-programthe Proceedings of the Eleventh International Workshop on Coding and Cryptography (WCC 2019), Saint-Jacut-de-la-Mer, France, March 31–April 5, 2019. Its presentation slides are available from https://www.slideshare.net/RyutarohMatsumoto.
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