On publicly verifiable secret sharing schemes
Secret sharing allows a dealer to distribute shares of a secret to a set of parties such that only so-called authorised subsets of these parties can recover the secret, whilst forbidden sets gain at most some restricted amount of information. This idea has been built upon in verifiable secret sharin...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/384705 |
| Acceso en línea: | https://hdl.handle.net/2117/384705 |
| Access Level: | acceso abierto |
| Palabra clave: | Cryptography Computer science -- Mathematics secret sharing publicly verifiable homomorphic voting Criptografia Informàtica -- Matemàtica Classificació AMS::94 Information And Communication, Circuits::94A Communication, information Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | Secret sharing allows a dealer to distribute shares of a secret to a set of parties such that only so-called authorised subsets of these parties can recover the secret, whilst forbidden sets gain at most some restricted amount of information. This idea has been built upon in verifiable secret sharing to allow parties to verify that their shares are valid and will therefore correctly reconstruct the same secret. This can then be further extended to publicly verifiable secret sharing by firstly considering only public channels of communication, hence imposing the need for encryption of the shares, and secondly by requiring that any party be able to verify any other parties shares from the public encryption. In this thesis we work our way up from the original secret sharing scheme by Shamir to examples of various approaches of publicly verifiable schemes. Due to the need for encryption in private communication, different cryptographic methods allow for certain interesting advantages in the schemes. We review some important existing methods and their significant properties of interest, such as being homomorphic or efficiently verifiable. We also consider recent improvements in these schemes and make a contribution by showing that an encryption scheme by Castagnos and Laguillaumie allows for a publicly verifiable secret sharing scheme to have some interesting homomorphic properties. To explore further we look at generalisations to the recently introduced idea of Abelian secret sharing, and we consider some examples of such constructions. Finally we look at some applications of secret sharing schemes, and present our own implementation of Schoenmaker’s scheme in Python, along with a voting system on which it is based. |
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