residuosity problem

См. также в других словарях:

• 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

• 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

• 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

• 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

• 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

• Okamoto–Uchiyama cryptosystem — The Okamoto–Uchiyama cryptosystem was discovered in 1998 by T. Okamoto and S. Uchiyama. The system works in the group , where n is of the form p2q and p and q are large primes. Contents 1 Scheme definition 1.1 Key generation …   Wikipedia

• Okamoto-Uchiyama cryptosystem — The Okamoto Uchiyama Cryptosystem was discovered in 1998 by T. Okamoto and S. Uchiyama. The system works in the group (mathbb{Z}/nmathbb{Z})^*, where n is of the form p 2 q . The Okamoto Uchiyama cryptosystem is a precursor to the Paillier… …   Wikipedia

• Cocks IBE scheme — is an Identity based encryption system proposed by Clifford Cocks in 2001 [1]. The security of the scheme is based on the hardness of the quadratic residuosity problem. Contents 1 Protocol 1.1 Setup 1.2 Extract …   Wikipedia