Ideal hierarchical secret sharing schemes
Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/95919 http://hdl.handle.net/10220/11464 |
| _version_ | 1826129237088665600 |
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| author | Farràs, Oriol Padró, Carles |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Farràs, Oriol Padró, Carles |
| author_sort | Farràs, Oriol |
| collection | NTU |
| description | Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization is based on the well-known connection between ideal secret sharing schemes and matroids and, more specifically, on the connection between ideal multipartite secret sharing schemes and integer polymatroids. In particular, we prove that every hierarchical matroid port admits an ideal linear secret sharing scheme over every large enough finite field. Finally, we use our results to present a new proof for the existing characterization of the ideal weighted threshold access structures. |
| first_indexed | 2024-10-01T07:37:22Z |
| format | Journal Article |
| id | ntu-10356/95919 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:37:22Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/959192020-03-07T12:37:22Z Ideal hierarchical secret sharing schemes Farràs, Oriol Padró, Carles School of Physical and Mathematical Sciences Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization is based on the well-known connection between ideal secret sharing schemes and matroids and, more specifically, on the connection between ideal multipartite secret sharing schemes and integer polymatroids. In particular, we prove that every hierarchical matroid port admits an ideal linear secret sharing scheme over every large enough finite field. Finally, we use our results to present a new proof for the existing characterization of the ideal weighted threshold access structures. 2013-07-15T08:25:45Z 2019-12-06T19:23:20Z 2013-07-15T08:25:45Z 2019-12-06T19:23:20Z 2011 2011 Journal Article Farràs, O., & Padró, C. (2012). Ideal Hierarchical Secret Sharing Schemes. IEEE Transactions on Information Theory, 58(5), 3273-3286. 0018-9448 https://hdl.handle.net/10356/95919 http://hdl.handle.net/10220/11464 10.1109/TIT.2011.2182034 en IEEE transactions on information theory © 2011 IEEE. |
| spellingShingle | Farràs, Oriol Padró, Carles Ideal hierarchical secret sharing schemes |
| title | Ideal hierarchical secret sharing schemes |
| title_full | Ideal hierarchical secret sharing schemes |
| title_fullStr | Ideal hierarchical secret sharing schemes |
| title_full_unstemmed | Ideal hierarchical secret sharing schemes |
| title_short | Ideal hierarchical secret sharing schemes |
| title_sort | ideal hierarchical secret sharing schemes |
| url | https://hdl.handle.net/10356/95919 http://hdl.handle.net/10220/11464 |
| work_keys_str_mv | AT farrasoriol idealhierarchicalsecretsharingschemes AT padrocarles idealhierarchicalsecretsharingschemes |