Naccache–Stern cryptosystem

The Naccache–Stern cryptosystem was discovered by David Naccache and Jacques Stern in 1998.

Like many public key cryptosystems, this scheme works in the group

This system allows encryption of a message m in the group

Then E(m) is an encryption of the message m. To decrypt, we first find m mod pi for each i, and then we apply the Chinese remainder theorem to calculate m mod

The semantic security of the Naccache–Stern cryptosystem rests on an extension of the quadratic residuosity problem known as the higher residuosity problem.

Naccache, David; Stern, Jacques (1998).

"A New Public Key Cryptosystem Based on Higher Residues".

Proceedings of the 5th ACM Conference on Computer and Communications Security.