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

Zhenfu Cao; Xiaolei Dong; Licheng Wang; Jun Shao

Paper 2013/569

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

Zhenfu Cao, Xiaolei Dong, 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.

Metadata

Available format(s): PDF
Publication info: Preprint. MINOR revision.
Keywords: Goldwasser-Micali cryptosystem $k^{th}$-power residuosity $k$-residue discrete logarithm additive homomorphism lossy trapdoor function
Contact author(s): zfcao @ cs sjtu edu cn
History: 2013-09-24: revised; 2013-09-09: received; See all versions
Short URL: https://ia.cr/2013/569
License: CC BY

BibTeX

@misc{cryptoeprint:2013/569,
      author = {Zhenfu Cao and Xiaolei Dong and Licheng Wang and Jun Shao},
      title = {More Efficient Cryptosystems From $k^{th}$-Power Residues},
      howpublished = {Cryptology {ePrint} Archive, Paper 2013/569},
      year = {2013},
      url = {https://eprint.iacr.org/2013/569}
}