词条 | Damgård–Jurik cryptosystem |
释义 |
The Damgård–Jurik cryptosystem[1] 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. Key generation
Encryption
Decryption
SimplificationAt the cost of no longer containing the classical Paillier cryptosystem as an instance, Damgård–Jurik can be simplified in the following way:
In this case decryption produces . Using recursive Paillier decryption this gives us directly the plaintext m. See also
References1. ^Ivan Damgård, Mads Jurik: A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System. Public Key Cryptography 2001: 119-136 {{Cryptography navbox | public-key}}{{DEFAULTSORT:Damgard-Jurik Cryptosystem}} 1 : Public-key encryption schemes |
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