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

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

Goldwasser–Micali cryptosystem         
ASYMMETRIC KEY ENCRYPTION ALGORITHM
Goldwasser-Micali; Goldwasser-Micali encryption; Goldwasser-Micali cryptosystem; Goldwasser-Micali encryption scheme
The Goldwasser–Micali (GM) cryptosystem is an asymmetric key encryption algorithm developed by Shafi Goldwasser and Silvio Micali in 1982. GM has the distinction of being the first probabilistic public-key encryption scheme which is provably secure under standard cryptographic assumptions.
Damgård–Jurik cryptosystem         
The Damgård–Jurik cryptosystemIvan Damgård, Mads Jurik: A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System. Public Key Cryptography 2001: 119-136 is a generalization of the Paillier cryptosystem.
Okamoto–Uchiyama cryptosystem         
The Okamoto–Uchiyama cryptosystem is a public key cryptosystem proposed in 1998 by Tatsuaki Okamoto and Shigenori Uchiyama. The system works in the multiplicative group of integers modulo n, (\mathbb{Z}/n\mathbb{Z})^*, where n is of the form p2q and p and q are large primes.

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.