Ideal secret sharing schemes with share selectability

  • Authors:
  • Keita Emura;Atsuko Miyaji;Akito Nomura;Mohammad Shahriar Rahman;Masakazu Soshi

  • Affiliations:
  • Center for Highly Dependable Embedded Systems Technology, Japan Advanced Institute of Science and Technology, Japan;School of Information Science, JAIST, Japan;Institute of Science and Engineering, Kanazawa University, Japan;School of Information Science, JAIST, Japan;Graduate School of Information Sciences, Hiroshima City University, Japan

  • Venue:
  • ICICS'11 Proceedings of the 13th international conference on Information and communications security
  • Year:
  • 2011

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Abstract

In this paper, we investigate a new concept, called share selectable secret sharing, where no unauthorized set can obtain information of the secret (in the information-theoretic sense) even if shares are selectable as arbitrary values which are independent of the secret. We propose two totally selectable (i.e., all users' shares are selectable) secret sharing schemes with unanimous structure. We also propose a quasiselectable (i.e., a part of each user's share is selectable) secret sharing scheme with certain hierarchical structures which contains special cases of the hierarchical threshold structures introduced by Tamir Tassa in TCC2004 (or its full version (J. Cryptology 2007)). If all selectable shares are randomly chosen, then our schemes are perfect. Finally, we discuss the effect of the leakage information of the secret if a weak secret is indicated as a selectable share.