The Damgård–Jurik cryptosystem is a generalization of the Paillier cryptosystem. It uses computations modulo where is an RSA modulus and a (positive) natural number. Paillier's scheme is the special case with . The order (Euler's totient function) of can be divided by . Moreover, can be written as the direct product of . is cyclic and of order , while is isomorphic to . For encryption, the message is transformed into the corresponding coset of the factor group and the security of the scheme relies on the difficulty of distinguishing random elements in different cosets of . It is semantically secure if it is hard to decide if two given elements are in the same coset. Like Paillier, the security of Damgård–Jurik can be proven under the decisional composite residuosity assumption.
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| - Damgård-Jurik-Kryptosystem (de)
- Damgård–Jurik cryptosystem (en)
- Криптосистема Дамгорда — Юрика (ru)
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| - Das Damgård-Jurik-Kryptosystem ist ein semantisch sicherer, asymmetrischer Verschlüsselungsalgorithmus. Es wurde 2001 an der Konferenz PKC von den beiden Kryptographen und vorgestellt. Das Verfahren ist additiv-homomorph, was bedeutet, dass durch die Multiplikation zweier Schlüsseltexte die Klartexte addiert werden. Es ist also nicht nötig, die Schlüsseltexte zu entschlüsseln, um auf den Klartexten operieren zu können.Das Verfahren ist ein Nachfolger des Paillier-Kryptosystems und enthält dieses als Spezialfall. (de)
- The Damgård–Jurik cryptosystem is a generalization of the Paillier cryptosystem. It uses computations modulo where is an RSA modulus and a (positive) natural number. Paillier's scheme is the special case with . The order (Euler's totient function) of can be divided by . Moreover, can be written as the direct product of . is cyclic and of order , while is isomorphic to . For encryption, the message is transformed into the corresponding coset of the factor group and the security of the scheme relies on the difficulty of distinguishing random elements in different cosets of . It is semantically secure if it is hard to decide if two given elements are in the same coset. Like Paillier, the security of Damgård–Jurik can be proven under the decisional composite residuosity assumption. (en)
- Криптосистема Дамгорда — Юрика — криптосистема с открытым ключом, предложенная Иваном Дамгордом и Мадсом Юриком в 2000 г. Является обобщением криптосистемы Пэйе для больших модулей с целью расширения области применения. (ru)
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| - Das Damgård-Jurik-Kryptosystem ist ein semantisch sicherer, asymmetrischer Verschlüsselungsalgorithmus. Es wurde 2001 an der Konferenz PKC von den beiden Kryptographen und vorgestellt. Das Verfahren ist additiv-homomorph, was bedeutet, dass durch die Multiplikation zweier Schlüsseltexte die Klartexte addiert werden. Es ist also nicht nötig, die Schlüsseltexte zu entschlüsseln, um auf den Klartexten operieren zu können.Das Verfahren ist ein Nachfolger des Paillier-Kryptosystems und enthält dieses als Spezialfall. (de)
- The Damgård–Jurik cryptosystem is a generalization of the Paillier cryptosystem. It uses computations modulo where is an RSA modulus and a (positive) natural number. Paillier's scheme is the special case with . The order (Euler's totient function) of can be divided by . Moreover, can be written as the direct product of . is cyclic and of order , while is isomorphic to . For encryption, the message is transformed into the corresponding coset of the factor group and the security of the scheme relies on the difficulty of distinguishing random elements in different cosets of . It is semantically secure if it is hard to decide if two given elements are in the same coset. Like Paillier, the security of Damgård–Jurik can be proven under the decisional composite residuosity assumption. (en)
- Криптосистема Дамгорда — Юрика — криптосистема с открытым ключом, предложенная Иваном Дамгордом и Мадсом Юриком в 2000 г. Является обобщением криптосистемы Пэйе для больших модулей с целью расширения области применения. (ru)
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