A variant of the cramer-shoup cryptosystem for groups of unknown order

Abstract

The Cramer-Shoup cryptosystem for groups of prime orderis a practical public-key cryptosystem, provably secure in the standardmodel under standard assumptions. This paper extends the cryptosystemfor groups of unknown order, namely the group of quadratic residuesmodulo a composed N. Two security results are: In the standard model,the scheme is provably secure if both the Decisional Diffie-Hellman assumptionfor QRN and the factorisation assumption for N hold. In therandom oracle model, the scheme is provably secure under the factorisationassumption by a quite efficient reduction.