IEICE TRANSACTIONS on Fundamentals
Linear Algebraic Approach to Strongly Secure Ramp Secret Sharing for General Access Structures with Application to Symmetric PIR
Summary :
Ramp secret sharing is a variant of secret sharing which can achieve better information ratio than perfect schemes by allowing some partial information on a secret to leak out. Strongly secure ramp schemes can control the amount of leaked information on the components of a secret. In this paper, we reduce the construction of strongly secure ramp secret sharing for general access structures to a linear algebraic problem. As a result, we show that previous results on strongly secure network coding imply two linear transformation methods to make a given linear ramp scheme strongly secure. They are explicit or provide a deterministic algorithm while the previous methods which work for any linear ramp scheme are non-constructive. In addition, we present a novel application of strongly secure ramp schemes to symmetric PIR in a multi-user setting. Our solution is advantageous over those based on a non-strongly secure scheme in that it reduces the amount of communication between users and servers and also the amount of correlated randomness that servers generate in the setup.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.3 pp.263-271
- Publication Date
- 2023/03/01
- Publicized
- 2022/09/13
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2022CIP0001
- Type of Manuscript
- Special Section PAPER (Special Section on Cryptography and Information Security)
- Category
Authors
Reo ERIGUCHI
The University of Tokyo
Noboru KUNIHIRO
University of Tsukuba
Koji NUIDA
Kyushu University
Keyword
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Reo ERIGUCHI, Noboru KUNIHIRO, Koji NUIDA, "Linear Algebraic Approach to Strongly Secure Ramp Secret Sharing for General Access Structures with Application to Symmetric PIR" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 3, pp. 263-271, March 2023, doi: 10.1587/transfun.2022CIP0001.
Abstract: Ramp secret sharing is a variant of secret sharing which can achieve better information ratio than perfect schemes by allowing some partial information on a secret to leak out. Strongly secure ramp schemes can control the amount of leaked information on the components of a secret. In this paper, we reduce the construction of strongly secure ramp secret sharing for general access structures to a linear algebraic problem. As a result, we show that previous results on strongly secure network coding imply two linear transformation methods to make a given linear ramp scheme strongly secure. They are explicit or provide a deterministic algorithm while the previous methods which work for any linear ramp scheme are non-constructive. In addition, we present a novel application of strongly secure ramp schemes to symmetric PIR in a multi-user setting. Our solution is advantageous over those based on a non-strongly secure scheme in that it reduces the amount of communication between users and servers and also the amount of correlated randomness that servers generate in the setup.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022CIP0001/_p
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@ARTICLE{e106-a_3_263,
author={Reo ERIGUCHI, Noboru KUNIHIRO, Koji NUIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Linear Algebraic Approach to Strongly Secure Ramp Secret Sharing for General Access Structures with Application to Symmetric PIR},
year={2023},
volume={E106-A},
number={3},
pages={263-271},
abstract={Ramp secret sharing is a variant of secret sharing which can achieve better information ratio than perfect schemes by allowing some partial information on a secret to leak out. Strongly secure ramp schemes can control the amount of leaked information on the components of a secret. In this paper, we reduce the construction of strongly secure ramp secret sharing for general access structures to a linear algebraic problem. As a result, we show that previous results on strongly secure network coding imply two linear transformation methods to make a given linear ramp scheme strongly secure. They are explicit or provide a deterministic algorithm while the previous methods which work for any linear ramp scheme are non-constructive. In addition, we present a novel application of strongly secure ramp schemes to symmetric PIR in a multi-user setting. Our solution is advantageous over those based on a non-strongly secure scheme in that it reduces the amount of communication between users and servers and also the amount of correlated randomness that servers generate in the setup.},
keywords={},
doi={10.1587/transfun.2022CIP0001},
ISSN={1745-1337},
month={March},}
Copy
TY - JOUR
TI - Linear Algebraic Approach to Strongly Secure Ramp Secret Sharing for General Access Structures with Application to Symmetric PIR
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 263
EP - 271
AU - Reo ERIGUCHI
AU - Noboru KUNIHIRO
AU - Koji NUIDA
PY - 2023
DO - 10.1587/transfun.2022CIP0001
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2023
AB - Ramp secret sharing is a variant of secret sharing which can achieve better information ratio than perfect schemes by allowing some partial information on a secret to leak out. Strongly secure ramp schemes can control the amount of leaked information on the components of a secret. In this paper, we reduce the construction of strongly secure ramp secret sharing for general access structures to a linear algebraic problem. As a result, we show that previous results on strongly secure network coding imply two linear transformation methods to make a given linear ramp scheme strongly secure. They are explicit or provide a deterministic algorithm while the previous methods which work for any linear ramp scheme are non-constructive. In addition, we present a novel application of strongly secure ramp schemes to symmetric PIR in a multi-user setting. Our solution is advantageous over those based on a non-strongly secure scheme in that it reduces the amount of communication between users and servers and also the amount of correlated randomness that servers generate in the setup.
ER -
English
