Optimal non-perfect uniform secret sharing schemes
| Autor: | Torben Brandt Hansen, Tarik Kaced, Carles Padró, Oriol Farràs |
|---|---|
| Přispěvatelé: | Garay , Juan, Gennaro , Rosario, Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
TheoryofComputation_MISCELLANEOUS
Homomorphic secret sharing Theoretical computer science 94 Information And Communication Circuits::94A Communication information [Classificació AMS] Sequences (Mathematics) Seqüències (Matemàtica) Key distribution Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC] Codificació Teoria de la Shared secret Secret sharing Shamir's Secret Sharing Information ratio Information Ratio Computer Science::Multimedia Secure multi-party computation Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant [Àrees temàtiques de la UPC] Verifiable secret sharing Coding theory Non-perfect secret sharing Polymatroid 62 Statistics::62L Sequential methods [Classificació AMS] Computer Science::Cryptography and Security Mathematics |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Farràs, O, Hansen, T B, Kaced, T & Padró, C 2014, Optimal non-perfect uniform secret sharing schemes . in J Garay & R Gennaro (eds), Advances in Cryptology – CRYPTO 2014 : 34th Annual Cryptology Conference, Santa Barbara, CA, USA, August 17-21, 2014, Proceedings, Part II . Springer, Lecture Notes in Computer Science, vol. 8617, pp. 217-234, Annual International Cryptology Conference, Santa Barbara, United States, 17/08/2014 . https://doi.org/10.1007/978-3-662-44381-1_13 Advances in Cryptology – CRYPTO 2014 ISBN: 9783662443804 CRYPTO (2) Recercat. Dipósit de la Recerca de Catalunya instname |
| DOI: | 10.1007/978-3-662-44381-1_13 |
| Popis: | A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this end, we extend the known connections between polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information that every subset of participants obtains about the secret value. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, the ones whose values depend only on the number of participants, generalize the threshold access structures. Our main result is to determine the optimal information ratio of the uniform access functions. Moreover, we present a construction of linear secret sharing schemes with optimal information ratio for the rational uniform access functions. |
| Databáze: | OpenAIRE |
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