founded on problems that are believed to be intractable. The higher residuosity problem (also called the nth-residuosity problem) is one such problem. This...

The quadratic residuosity problem (QRP) in computational number theory is to decide, given integers a {\displaystyle a} and N {\displaystyle N} , whether...

(decisional composite residuosity problem) Benaloh cryptosystem (higher residuosity problem) Naccache–Stern cryptosystem (higher residuosity problem) For a composite...

\,} Quadratic residuosity problem Higher residuosity problem P. Paillier, Public-Key Cryptosystems Based on Composite Degree Residuosity Classes, Eurocrypt...

homomorphic public-key cryptosystem whose security rests on the higher residuosity problem. The Naccache–Stern cryptosystem was discovered by David Naccache...

order p. This is very similar to the quadratic residuosity problem and the higher residuosity problem. Okamoto, Tatsuaki; Uchiyama, Shigenori (1998)....

must be coprime to the modulus. Gauss used R and N to denote residuosity and non-residuosity, respectively; for example, 2 R 7 and 5 N 7, or 1 R 8 and 3...

cryptography. The problem of computing n-th residue classes is believed to be computationally difficult. The decisional composite residuosity assumption is...

{r}})} time and space. The security of this scheme rests on the Higher residuosity problem, specifically, given z,r and n where the factorization of n is...

reduced to solving some hard mathematical problem (e.g., Decisional Diffie-Hellman or the Quadratic Residuosity Problem). Other, semantically insecure algorithms...

based on the difficulty of the quadratic residuosity problem. Since the only known way to solve that problem is to factor the modulus, it is generally...

cryptographic protocols used by Schindelhauer are based on quadratic residuosity, and the general scheme is similar in spirit to the above protocol. The...