# 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 *n*^{2} or not, i.e., whether there exists *y* such that

## See also

## References

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

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