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Paper 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.

Metadata
Available format(s)
PDF PS
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
public-key cryptographycomplexity theoryfactoring assumption
Contact author(s)
lucks @ th informatik uni-mannheim de
History
2002-06-18: last of 2 revisions
2002-04-25: received
See all versions
Short URL
https://ia.cr/2002/052
License
Creative Commons Attribution
CC BY
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