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 método de matriz linear Piece In Hand (PH, abreviadamente) com variáveis aleatórias foi proposto em nosso trabalho anterior. É uma prescrição geral que pode ser aplicável a qualquer tipo de criptossistema multivariado de chave pública com o objetivo de aumentar a sua segurança. Na verdade, mostramos, de forma experimental, que o método da matriz linear PH com variáveis aleatórias pode certamente aumentar a segurança do HFE contra o ataque à base de Grobner, onde o HFE é uma das principais variantes de criptossistemas multivariados de chave pública. Em 1998, Patarin, Goubin e Courtois introduziram o método plus como uma prescrição geral que visa aumentar a segurança de qualquer MPKC, assim como o método linear da matriz PH com variáveis aleatórias. Neste artigo provamos a equivalência entre o método plus e o método da matriz linear primitiva PH, que é introduzido pelo nosso trabalho anterior para explicar a noção do método da matriz PH em geral de uma forma ilustrativa e não para um uso prático para melhorar o segurança de qualquer MPKC. Com base nesta equivalência, mostramos que o método linear da matriz PH com variáveis aleatórias tem vantagem substancial sobre o método plus no que diz respeito ao aumento da segurança. No método da matriz linear PH com variáveis aleatórias, as três matrizes, incluindo a matriz PH, desempenham um papel central na chave secreta e na chave pública. Neste artigo, esclarecemos como gerar essas matrizes e, assim, apresentamos dois algoritmos probabilísticos de tempo polinomial para gerar essas matrizes. Em particular, o segundo tem uma forma concisa e é obtido como subproduto da prova da equivalência entre o método plus e o método da matriz PH linear primitiva.
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Kohtaro TADAKI, Shigeo TSUJII, "Key-Generation Algorithms for Linear Piece In Hand Matrix Method" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 6, pp. 1102-1110, June 2010, doi: 10.1587/transfun.E93.A.1102.
Abstract: The linear Piece In Hand (PH, for short) matrix method with random variables was proposed in our former work. It is a general prescription which can be applicable to any type of multivariate public-key cryptosystems for the purpose of enhancing their security. Actually, we showed, in an experimental manner, that the linear PH matrix method with random variables can certainly enhance the security of HFE against the Grobner basis attack, where HFE is one of the major variants of multivariate public-key cryptosystems. In 1998 Patarin, Goubin, and Courtois introduced the plus method as a general prescription which aims to enhance the security of any given MPKC, just like the linear PH matrix method with random variables. In this paper we prove the equivalence between the plus method and the primitive linear PH matrix method, which is introduced by our previous work to explain the notion of the PH matrix method in general in an illustrative manner and not for a practical use to enhance the security of any given MPKC. Based on this equivalence, we show that the linear PH matrix method with random variables has the substantial advantage over the plus method with respect to the security enhancement. In the linear PH matrix method with random variables, the three matrices, including the PH matrix, play a central role in the secret-key and public-key. In this paper, we clarify how to generate these matrices and thus present two probabilistic polynomial-time algorithms to generate these matrices. In particular, the second one has a concise form, and is obtained as a byproduct of the proof of the equivalence between the plus method and the primitive linear PH matrix method.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.1102/_p
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@ARTICLE{e93-a_6_1102,
author={Kohtaro TADAKI, Shigeo TSUJII, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Key-Generation Algorithms for Linear Piece In Hand Matrix Method},
year={2010},
volume={E93-A},
number={6},
pages={1102-1110},
abstract={The linear Piece In Hand (PH, for short) matrix method with random variables was proposed in our former work. It is a general prescription which can be applicable to any type of multivariate public-key cryptosystems for the purpose of enhancing their security. Actually, we showed, in an experimental manner, that the linear PH matrix method with random variables can certainly enhance the security of HFE against the Grobner basis attack, where HFE is one of the major variants of multivariate public-key cryptosystems. In 1998 Patarin, Goubin, and Courtois introduced the plus method as a general prescription which aims to enhance the security of any given MPKC, just like the linear PH matrix method with random variables. In this paper we prove the equivalence between the plus method and the primitive linear PH matrix method, which is introduced by our previous work to explain the notion of the PH matrix method in general in an illustrative manner and not for a practical use to enhance the security of any given MPKC. Based on this equivalence, we show that the linear PH matrix method with random variables has the substantial advantage over the plus method with respect to the security enhancement. In the linear PH matrix method with random variables, the three matrices, including the PH matrix, play a central role in the secret-key and public-key. In this paper, we clarify how to generate these matrices and thus present two probabilistic polynomial-time algorithms to generate these matrices. In particular, the second one has a concise form, and is obtained as a byproduct of the proof of the equivalence between the plus method and the primitive linear PH matrix method.},
keywords={},
doi={10.1587/transfun.E93.A.1102},
ISSN={1745-1337},
month={June},}
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TY - JOUR
TI - Key-Generation Algorithms for Linear Piece In Hand Matrix Method
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1102
EP - 1110
AU - Kohtaro TADAKI
AU - Shigeo TSUJII
PY - 2010
DO - 10.1587/transfun.E93.A.1102
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2010
AB - The linear Piece In Hand (PH, for short) matrix method with random variables was proposed in our former work. It is a general prescription which can be applicable to any type of multivariate public-key cryptosystems for the purpose of enhancing their security. Actually, we showed, in an experimental manner, that the linear PH matrix method with random variables can certainly enhance the security of HFE against the Grobner basis attack, where HFE is one of the major variants of multivariate public-key cryptosystems. In 1998 Patarin, Goubin, and Courtois introduced the plus method as a general prescription which aims to enhance the security of any given MPKC, just like the linear PH matrix method with random variables. In this paper we prove the equivalence between the plus method and the primitive linear PH matrix method, which is introduced by our previous work to explain the notion of the PH matrix method in general in an illustrative manner and not for a practical use to enhance the security of any given MPKC. Based on this equivalence, we show that the linear PH matrix method with random variables has the substantial advantage over the plus method with respect to the security enhancement. In the linear PH matrix method with random variables, the three matrices, including the PH matrix, play a central role in the secret-key and public-key. In this paper, we clarify how to generate these matrices and thus present two probabilistic polynomial-time algorithms to generate these matrices. In particular, the second one has a concise form, and is obtained as a byproduct of the proof of the equivalence between the plus method and the primitive linear PH matrix method.
ER -