On Asymptotically Good Ramp Secret Sharing Schemes

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

doi:10.1587/transfun.E100.A.2699

On Asymptotically Good Ramp Secret Sharing Schemes

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

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.12 pp.2699-2708

Publication Date: 2017/12/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.2699

Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Cryptography and Information Security

Authors

Olav GEIL
  Aalborg University
Stefano MARTIN
  Aalborg University
Umberto MARTÍNEZ-PEÑAS
  Aalborg University
Ryutaroh MATSUMOTO
  Aalborg University,Nagoya University
Diego RUANO
  Aalborg University

Keyword

algebraic geometric codes, generalized Hamming weights, relative generalized Hamming weights, secret sharing

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Olav GEIL, Stefano MARTIN, Umberto MARTÍNEZ-PEÑAS, Ryutaroh MATSUMOTO, Diego RUANO, "On Asymptotically Good Ramp Secret Sharing Schemes" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 12, pp. 2699-2708, December 2017, doi: 10.1587/transfun.E100.A.2699.
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2699/_p

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@ARTICLE{e100-a_12_2699,
author={Olav GEIL, Stefano MARTIN, Umberto MARTÍNEZ-PEÑAS, Ryutaroh MATSUMOTO, Diego RUANO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On Asymptotically Good Ramp Secret Sharing Schemes},
year={2017},
volume={E100-A},
number={12},
pages={2699-2708},
abstract={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.},
keywords={},
doi={10.1587/transfun.E100.A.2699},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - On Asymptotically Good Ramp Secret Sharing Schemes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2699
EP - 2708
AU - Olav GEIL
AU - Stefano MARTIN
AU - Umberto MARTÍNEZ-PEÑAS
AU - Ryutaroh MATSUMOTO
AU - Diego RUANO
PY - 2017
DO - 10.1587/transfun.E100.A.2699
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2017
AB - 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.
ER -