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**Quadratic residuosity problem**— The quadratic residuosity problem in computational number theory is the question of distinguishing by calculation the quadratic residues in modular arithmetic for a modulus N , where N is a composite number. This is an important consideration in… … Wikipedia**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… … Wikipedia**Higher residuosity problem**— In cryptography most public key cryptosystems are founded on problems that are believed to be intractable. The higher residuosity problem is one such problem. This problem is easier to solve than integer factorization, so the assumption that this … Wikipedia**Paillier cryptosystem**— The Paillier cryptosystem, named after and invented by 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. This… … Wikipedia**IP (complexity)**— In computational complexity theory, the class IP is the class of problems solvable by an interactive proof system. The concept of an interactive proof system was first introduced by Goldwasser, et al. in 1985. An interactive proof system consists … Wikipedia**Naccache-Stern cryptosystem**— Note: this is not to be confused with the Naccache Stern knapsack cryptosystem.The Naccache Stern cryptosystem is a homomorphic Public key cryptosystem whose security rests on the higher residuosity problem.The Naccache Stern cryptosystem was… … Wikipedia**Computational hardness assumption**— In cryptography, a major goal is to create cryptographic primitives with provable security. In some cases cryptographic protocols are found to have information theoretic security, the one time pad is a common example. In many cases, information… … Wikipedia**Naccache–Stern cryptosystem**— Note: this is not to be confused with the Naccache–Stern knapsack cryptosystem. The Naccache–Stern cryptosystem is a homomorphic public key cryptosystem whose security rests on the higher residuosity problem. The Naccache–Stern cryptosystem was… … Wikipedia**Quadratic residue**— In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract… … Wikipedia**Goldwasser-Micali cryptosystem**— The Goldwasser Micali cryptosystem (GM) is an asymmetric key encryption algorithm developed by Shafi Goldwasser and Silvio Micali in 1982. GM has the distinction of being the first probabilistic public key encryption scheme which is provably… … Wikipedia