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Title:
A Variant of the Cramer-Shoup Cryptosystem for Groups with Unknwon Order
Authors: 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.
ePrint: https://eprint.iacr.org/2002/052
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