Cryptology ePrint Archive: Report 2002/052

A Variant of the Cramer-Shoup Cryptosystem for Groups with Unknwon Order

Stefan Lucks

Abstract: The Cramer-Shoup cryptosystem for groups of prime order is a practical public-key cryptosystem, provably secure in the standard model under standard assumptions. This paper extends the cryptosystem for groups of unknown order, namely the group of quadratic residues modulo a composed N. Two security results are: In the standard model, the scheme is provably secure if both the Decisional Diffie-Hellman assumption for QR_N *and* the factorisation assumption for N hold. In the random oracle model, the security of the scheme is provable by a quite efficient reduction.

Category / Keywords: public-key cryptography / public-key cryptography, complexity theory, factoring assumption

Date: received 25 Apr 2002, last revised 18 Jun 2002

Contact author: lucks at th informatik uni-mannheim de

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Version: 20020618:171425 (All versions of this report)

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