Geometric and Computational Approach to Classical and Quantum Secret Sharing

  • Ryutaroh Matsumoto
  • Diego Ruano
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 198)


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 \(C_2 \subset C_1 \subset \mathbf {F}_q^n\). On the other hand, a nest code pair \(C_2 \subset C_1 \subset \mathbf {F}_q^n\) 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.


Algebraic geometry codes Quantum secret sharing Access structure 



The authors gratefully acknowledge the support from Japan Society for the Promotion of Science (Grant Nos. 23246071 and 26289116), from the Spanish MINECO/FEDER (Grant No. MTM2012-36917-C03-03 and No. MTM2015-65764-C3-2-P), the Danish Council for Independent Research (Grant No. DFF-4002-00367) and from the “Program for Promoting the Enhancement of Research Universities” at Tokyo Institute of Technology.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Communications and Computer EngineeringTokyo Institute of TechnologyTokyoJapan
  2. 2.Department of Mathematical SciencesAalborg UniversityAalborgDenmark

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