On Asymptotically Good Ramp Secret Sharing Schemes

Olav GEIL  Stefano MARTIN  Umberto MARTÍNEZ-PEÑAS  Ryutaroh MATSUMOTO  Diego RUANO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.12   pp.2699-2708
Publication Date: 2017/12/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Cryptography and Information Security
Keyword: 
algebraic geometric codes,  generalized Hamming weights,  relative generalized Hamming weights,  secret sharing,  

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Summary: 
Asymptotically good sequences of linear ramp secret sharing schemes have been intensively studied by Cramer et al. in terms of sequences of pairs of nested algebraic geometric codes [4]-[8], [10]. In those works the focus is on full privacy and full reconstruction. In this paper we analyze additional parameters describing the asymptotic behavior of partial information leakage and possibly also partial reconstruction giving a more complete picture of the access structure for sequences of linear ramp secret sharing schemes. Our study involves a detailed treatment of the (relative) generalized Hamming weights of the considered codes.