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 a n-residue modulo n² or not, i.e., whether there exists y such that