On publicly verifiable secret sharing schemes
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/384705
Correu electrònic de l'autorJEREMYLVL.WORKGMAIL.COM
Tipus de documentProjecte Final de Màster Oficial
Data2023-01
Condicions d'accésAccés obert
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continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
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Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacional
Abstract
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.
TitulacióMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)
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