The decisional composite residuosity assumption (DCRA) is a mathematical assumption used in

cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...

. In particular, the assumption is used in the proof of the

Paillier cryptosystem The Paillier cryptosystem, invented by and named after Pascal Paillier in 1999, is a probabilistic asymmetric algorithm for public key cryptography. The problem of computing ''n''-th residue classes is believed to be computationally difficult. Th ...

. Informally, the DCRA states that given a

composite Composite or compositing may refer to: Materials * Composite material, a material that is made from several different substances ** Metal matrix composite, composed of metal and other parts ** Cermet, a composite of ceramic and metallic material ...

n

and an

integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

z

, it is hard to decide whether

z

is an

n

-residue

modulo In computing and mathematics, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, the latter being called the '' modulus'' of the operation. Given two positive numbers and , mo ...

n^2

. ''I.e.'' whether there exists a

y

such that :

z \equiv y^n \pmod. \,

References

* P. Paillier, ''Public-Key Cryptosystems Based on Composite Degree Residuosity Classes'', Eurocrypt 1999. {{DEFAULTSORT:Decisional Composite Residuosity Assumption Computational hardness assumptions

See also

References