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".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Primeiro consideramos uma variante do esquema de criptografia Schmidt-Samoa-Takagi sem perder propriedades aditivamente homomórficas. Mostramos que esta variante é segura no sentido de IND-CPA sob a suposição de residuosidade composta decisória, e de OW-CPA sob a suposição sobre a dureza do factoring n=p2q. Em segundo lugar, introduzimos novas propriedades algébricas “afins” e “restrição de pré-imagem”, que estão intimamente relacionadas com a homomorficidade. Intuitivamente, "afim" é uma tupla de funções que possuem uma propriedade homomórfica especial, e "restrição de pré-imagem" é uma função que pode restringir o receptor a ter informações sobre a mensagem criptografada. Então, propomos um esquema de criptografia com raízes de potência primitivas da unidade em (Z/ns+1)
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Takato HIRANO, Koichiro WADA, Keisuke TANAKA, "Primitive Power Roots of Unity and Its Application to Encryption" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 8, pp. 1836-1844, August 2009, doi: 10.1587/transfun.E92.A.1836.
Abstract: We first consider a variant of the Schmidt-Samoa-Takagi encryption scheme without losing additively homomorphic properties. We show that this variant is secure in the sense of IND-CPA under the decisional composite residuosity assumption, and of OW-CPA under the assumption on the hardness of factoring n=p2q. Second, we introduce new algebraic properties "affine" and "pre-image restriction," which are closely related to homomorphicity. Intuitively, "affine" is a tuple of functions which have a special homomorphic property, and "pre-image restriction" is a function which can restrict the receiver to having information on the encrypted message. Then, we propose an encryption scheme with primitive power roots of unity in (Z/ns+1)
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.1836/_p
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@ARTICLE{e92-a_8_1836,
author={Takato HIRANO, Koichiro WADA, Keisuke TANAKA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Primitive Power Roots of Unity and Its Application to Encryption},
year={2009},
volume={E92-A},
number={8},
pages={1836-1844},
abstract={We first consider a variant of the Schmidt-Samoa-Takagi encryption scheme without losing additively homomorphic properties. We show that this variant is secure in the sense of IND-CPA under the decisional composite residuosity assumption, and of OW-CPA under the assumption on the hardness of factoring n=p2q. Second, we introduce new algebraic properties "affine" and "pre-image restriction," which are closely related to homomorphicity. Intuitively, "affine" is a tuple of functions which have a special homomorphic property, and "pre-image restriction" is a function which can restrict the receiver to having information on the encrypted message. Then, we propose an encryption scheme with primitive power roots of unity in (Z/ns+1)
keywords={},
doi={10.1587/transfun.E92.A.1836},
ISSN={1745-1337},
month={August},}
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TY - JOUR
TI - Primitive Power Roots of Unity and Its Application to Encryption
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1836
EP - 1844
AU - Takato HIRANO
AU - Koichiro WADA
AU - Keisuke TANAKA
PY - 2009
DO - 10.1587/transfun.E92.A.1836
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2009
AB - We first consider a variant of the Schmidt-Samoa-Takagi encryption scheme without losing additively homomorphic properties. We show that this variant is secure in the sense of IND-CPA under the decisional composite residuosity assumption, and of OW-CPA under the assumption on the hardness of factoring n=p2q. Second, we introduce new algebraic properties "affine" and "pre-image restriction," which are closely related to homomorphicity. Intuitively, "affine" is a tuple of functions which have a special homomorphic property, and "pre-image restriction" is a function which can restrict the receiver to having information on the encrypted message. Then, we propose an encryption scheme with primitive power roots of unity in (Z/ns+1)
ER -