symmetric cryptosystem - meaning and definition. What is symmetric cryptosystem
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What (who) is symmetric cryptosystem - definition

Damgaard-Jurik cryptosystem; Damgaard–Jurik cryptosystem; Damgård-Jurik cryptosystem; Damgard–Jurik cryptosystem; Damgard-Jurik cryptosystem

Symmetric-key algorithm         
ALGORITHM
Symmetric Algorithms; Symmetric key; Symmetric encryption; Symmetric key cryptography; Symmetric cypher; Shared key; Symmetric cipher; Symmetric-key cipher; Symmetric key algorithms; Symmetric cryptography; Private-key cryptography; Symmetric key encryption; Symmetric key algorithm; Reciprocal cipher; Reciprocal encipherment; Private key cryptography; Symmetric-key encryption algorithm; Symmetric-key cryptography; Private-key; Symmetric algorithm; Private-key encryption; Symmetrical encryption
Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both the encryption of plaintext and the decryption of ciphertext. The keys may be identical, or there may be a simple transformation to go between the two keys.
symmetric key cryptography         
ALGORITHM
Symmetric Algorithms; Symmetric key; Symmetric encryption; Symmetric key cryptography; Symmetric cypher; Shared key; Symmetric cipher; Symmetric-key cipher; Symmetric key algorithms; Symmetric cryptography; Private-key cryptography; Symmetric key encryption; Symmetric key algorithm; Reciprocal cipher; Reciprocal encipherment; Private key cryptography; Symmetric-key encryption algorithm; Symmetric-key cryptography; Private-key; Symmetric algorithm; Private-key encryption; Symmetrical encryption
<cryptography> A cryptography system in which both parties have the same encryption key, as in {secret key cryptography}. Opposite: public-key cryptography. (1998-06-09)
private-key cryptography         
ALGORITHM
Symmetric Algorithms; Symmetric key; Symmetric encryption; Symmetric key cryptography; Symmetric cypher; Shared key; Symmetric cipher; Symmetric-key cipher; Symmetric key algorithms; Symmetric cryptography; Private-key cryptography; Symmetric key encryption; Symmetric key algorithm; Reciprocal cipher; Reciprocal encipherment; Private key cryptography; Symmetric-key encryption algorithm; Symmetric-key cryptography; Private-key; Symmetric algorithm; Private-key encryption; Symmetrical encryption
<cryptography> As opposed to public-key cryptography, a cryptographic method in which the same key is used to encrypt and decrypt the message. Private-key algorithms include the obsolescent Data Encryption Standard (DES), triple-DES (3DES), the Advanced Encryption Standard (AES), also known as Rijndael, Blowfish, Twofish RC2, RC4, RC5 and RC6. A problem with private-key cryptography is that the sender and the recipient of the message must agree on a common key via some alternative secure channel. Public-key cryptography gives an answer to this problem. (2008-02-07)

Wikipedia

Damgård–Jurik cryptosystem

The Damgård–Jurik cryptosystem is a generalization of the Paillier cryptosystem. It uses computations modulo n s + 1 {\displaystyle n^{s+1}} where n {\displaystyle n} is an RSA modulus and s {\displaystyle s} a (positive) natural number. Paillier's scheme is the special case with s = 1 {\displaystyle s=1} . The order φ ( n s + 1 ) {\displaystyle \varphi (n^{s+1})} (Euler's totient function) of Z n s + 1 {\displaystyle Z_{n^{s+1}}^{*}} can be divided by n s {\displaystyle n^{s}} . Moreover, Z n s + 1 {\displaystyle Z_{n^{s+1}}^{*}} can be written as the direct product of G × H {\displaystyle G\times H} . G {\displaystyle G} is cyclic and of order n s {\displaystyle n^{s}} , while H {\displaystyle H} is isomorphic to Z n {\displaystyle Z_{n}^{*}} . For encryption, the message is transformed into the corresponding coset of the factor group G × H / H {\displaystyle G\times H/H} and the security of the scheme relies on the difficulty of distinguishing random elements in different cosets of H {\displaystyle H} . 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.