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Secret Sharing Schemes with Algebraic Properties and Applications

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Book cover Pursuit of the Universal (CiE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9709))

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Abstract

Secret sharing concerns the distribution of some secret information among a number of parties and is among the most well known tools in cryptography. Secret sharing schemes with certain additional algebraic properties, known as linearity and multiplicativity, have important applications in the area of secure multiparty computation and other areas such as zero knowledge proofs. Secret sharing also has a strong relationship with coding theory and motivates new problems in that field. I will survey several of the recent results in the area and some of their applications.

A major part of this work was written while the author was working at the Department of Computer Science, Aarhus University, Denmark.

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Notes

  1. 1.

    Furthermore, in the case \(k>1\), one can replace the k evaluation points for the secret by a primitive element of the extension field \(\mathbb {F}_{q^k}\), whereby one only needs \(n\le q-1\), and the privacy and reconstruction thresholds are preserved. The multiplicativity properties hold now with respect to the product in \(\mathbb {F}_{q^k}\) (for the secrets) instead of the coordinate-wise product in \(\mathbb {F}_q^k\).

  2. 2.

    Here we suppose each pair of players is connected by a secure point-to-point channel, but we do not assume the existence of a broadcast channel.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Aalborg University, Aalborg, Denmark

    Ignacio Cascudo

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  1. Ignacio Cascudo
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Correspondence to Ignacio Cascudo .

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Editors and Affiliations

  1. Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. Université Paris-Diderot - Paris 7, Paris, France

    Laurent Bienvenu

  3. University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

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Cascudo, I. (2016). Secret Sharing Schemes with Algebraic Properties and Applications. In: Beckmann, A., Bienvenu, L., Jonoska, N. (eds) Pursuit of the Universal. CiE 2016. Lecture Notes in Computer Science(), vol 9709. Springer, Cham. https://doi.org/10.1007/978-3-319-40189-8_7

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  • DOI: https://doi.org/10.1007/978-3-319-40189-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40188-1

  • Online ISBN: 978-3-319-40189-8

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