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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 number|composite]]&nbsp;''n'' and an [[integer]] ''z'', it is hard to decide whether ''z'' is a ''n''-residue [[modular arithmetic|modulo]]&nbsp;''n''<sup>2</sup> or not, i.e., whether there exists ''y'' such that


: <math>z \equiv y^n \pmod{n^2}. \, </math>
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== See also ==
* [[Computational hardness assumption]]
* [[Quadratic residuosity problem]]
* [[Higher residuosity problem]]
 
== References ==
* P. Paillier, ''Public-Key Cryptosystems Based on Composite Degree Residuosity Classes'', Eurocrypt 1999.
 
{{DEFAULTSORT:Decisional Composite Residuosity Assumption}}
[[Category:Computational hardness assumptions]]

Latest revision as of 08:29, 16 November 2014


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