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Geometric and computational approach to classical and quantum secret sharing. (English) Zbl 1383.81075
Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 267-272 (2017).
Summary: Secret sharing is a cryptographic scheme to encode a secret to multiple shares being distributed to participants, so that only qualified (or authorized) sets of participants can reconstruct the original secret from their shares. It is also known that every linear ramp secret sharing can be expressed by a nested pair of linear codes \(C_2 \subset C_1 \subset \mathbb{F}_q^n\). On the other hand, a nest code pair \(C_2 \subset C_1 \subset \mathbb{F}_q^n\) can also give a quantum secret sharing. Since \(C_1\) and \(C_2\) are linear codes, it is natural to use algebraic geometry codes to construct \(C_1\) and \(C_2\). The purpose of this work is to find sufficient conditions for qualified or forbidden sets by using geometric properties of the set of points.
For the entire collection see [Zbl 1379.13001].
MSC:
81P94 Quantum cryptography (quantum-theoretic aspects)
94A62 Authentication, digital signatures and secret sharing
94A60 Cryptography
94B05 Linear codes, general
81P70 Quantum coding (general)
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