Decisional composite residuosity assumption

The decisional composite residuosity assumption (DCRA) is a mathematical assumption used in cryptography. In particular, the assumption is used in the proof of the Paillier cryptosystem.

Informally, the DCRA states that given a composite $n$ and an integer $z$ , it is hard to decide whether $z$ is an $n$ -residue modulo $n^{2}$ . I.e. whether there exists a $y$ such that

z\equiv y^{n}{\pmod {n^{2}}}.\,

References

P. Paillier, Public-Key Cryptosystems Based on Composite Degree Residuosity Classes, Eurocrypt 1999.

v t e Computational hardness assumptions
Number theoretic	Integer factorization Phi-hiding RSA problem Strong RSA Quadratic residuosity Decisional composite residuosity Higher residuosity
Group theoretic	Discrete logarithm Diffie-Hellman Decisional Diffie–Hellman Computational Diffie–Hellman
Pairings	External Diffie–Hellman Sub-group hiding Decision linear
Lattices	Shortest vector problem (gap) Closest vector problem (gap) Learning with errors Ring learning with errors Short integer solution
Non-cryptographic	Exponential time hypothesis Unique games conjecture Planted clique conjecture

See also

References