## Cryptology ePrint Archive: Report 2013/569

More Efficient Cryptosystems From $k^{th}$-Power Residues

Zhenfu Cao and Xiaolei Dong and Licheng Wang and Jun Shao

Abstract: At Eurocrypt 2013, Joye and Libert proposed a method for constructing public key cryptosystems (PKCs) and lossy trapdoor functions (LTDFs) from $(2^\alpha)^{th}$-power residue symbols. Their work can be viewed as non-trivial extensions of the well-known PKC scheme due to Goldwasser and Micali, and the LTDF scheme due to Freeman et al., respectively. In this paper, we will demonstrate that this kind of work can be extended \emph{more generally}: all related constructions can work for any $k^{th}$-power residues if $k$ only contains small prime factors, instead of $(2^\alpha)^{th}$-power residues only. The resultant PKCs and LTDFs are more efficient than that from Joye-Libert method in terms of decryption speed with the same message length.

Category / Keywords: Goldwasser-Micali cryptosystem, $k^{th}$-power residuosity, $k$-residue discrete logarithm, additive homomorphism, lossy trapdoor function

Date: received 6 Sep 2013, last revised 24 Sep 2013

Contact author: zfcao at cs sjtu edu cn

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Short URL: ia.cr/2013/569

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