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 QRN and the factorisation assumption for N hold. In the random oracle model, the scheme is provably secure under the factorisation assumption by a quite efficient reduction.
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Lucks, S. (2002). A Variant of the Cramer-Shoup Cryptosystem for Groups of Unknown Order. In: Zheng, Y. (eds) Advances in Cryptology — ASIACRYPT 2002. ASIACRYPT 2002. Lecture Notes in Computer Science, vol 2501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36178-2_2
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DOI: https://doi.org/10.1007/3-540-36178-2_2
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