Abstract
At Eurocrypt ‘02 Cramer and Shoup [7] proposed a general paradigm to construct practical public-key cryptosystems secure against adaptive chosen-ciphertext attacks as well as several concrete examples. Among the others they presented a variant of Paillier’s [21] scheme achieving such a strong security requirement and for which two, independent, decryption mechanisms are allowed. In this paper we revisit such scheme and show that by considering a different subgroup, one can obtain a different scheme (whose security can be proved with respect to a different mathematical assumption) that allows for interesting applications. In particular we show how to construct a perfectly hiding commitment schemes that allows for an on-line / off-line efficiency tradeoff. The scheme is computationally binding under the assumption that factoring is hard, thus improving on the previous construction by Catalano et al. [5] whose binding property was based on the assumption that inverting RSA[N,N] (i.e. RSA with the public exponent set to N) is hard.
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Bresson, E., Catalano, D., Pointcheval, D. (2003). A Simple Public-Key Cryptosystem with a Double Trapdoor Decryption Mechanism and Its Applications. In: Laih, CS. (eds) Advances in Cryptology - ASIACRYPT 2003. ASIACRYPT 2003. Lecture Notes in Computer Science, vol 2894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40061-5_3
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DOI: https://doi.org/10.1007/978-3-540-40061-5_3
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