The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
O compartilhamento de segredo em rampa é uma variante do compartilhamento de segredo que pode alcançar uma melhor proporção de informações do que esquemas perfeitos, permitindo que algumas informações parciais sobre um segredo vazem. Esquemas de rampa fortemente seguros podem controlar a quantidade de informações vazadas sobre os componentes de um segredo. Neste artigo, reduzimos a construção de compartilhamento de segredo de rampa fortemente seguro para estruturas de acesso geral a um problema algébrico linear. Como resultado, mostramos que os resultados anteriores sobre codificação de rede fortemente segura implicam dois métodos de transformação linear para tornar um determinado esquema de rampa linear fortemente seguro. Eles são explícitos ou fornecem um algoritmo determinístico, enquanto os métodos anteriores que funcionam para qualquer esquema de rampa linear são não construtivos. Além disso, apresentamos uma nova aplicação de esquemas de rampa fortemente seguros para PIR simétrico em um ambiente multiusuário. Nossa solução é vantajosa em relação àquelas baseadas em um esquema não fortemente seguro, pois reduz a quantidade de comunicação entre usuários e servidores e também a quantidade de aleatoriedade correlacionada que os servidores geram na configuração.
Reo ERIGUCHI
The University of Tokyo
Noboru KUNIHIRO
University of Tsukuba
Koji NUIDA
Kyushu University
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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},}
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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 -