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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 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

See also[]

  • Computational hardness assumption
  • Quadratic residuosity problem
  • Higher residuosity problem


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