On asymptotically good ramp secret sharing schemes
Résumé
Asymptotically good sequences of ramp secret sharing schemes have been intensively studied by Cramer et al. in [1,2,3,4,5,6,7,8]. In those works the focus is on full privacy and full reconstruction. We propose an alternative definition of asymptotically good sequences of ramp secret sharing schemes where a small amount of information leakage is allowed (and possibly also non-full recovery). By a non-constructive proof we demonstrate the existence of sequences that – following our definition of goodness – have parameters arbitrary close to the optimal ones. Moreover – still using our definition – we demonstrate how to concretely construct asymptotically good sequences of schemes from sequences of algebraic geometric codes related to a tower of function fields. Our study involves a detailed treatment of the relative generalized Hamming weights of the involved codes.
Domaines
Cryptographie et sécurité [cs.CR]
Origine : Fichiers produits par l'(les) auteur(s)
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