Elliptic curve Paillier schemes

Steven D Galbraith

Paper 2001/050

Elliptic curve Paillier schemes

Steven D Galbraith

Abstract

This paper is concerned with generalisations of Paillier's probabilistic encryption scheme from the integers modulo a square to elliptic curves over rings. Paillier himself described two public key encryption schemes based on anomalous elliptic curves over rings. It is argued that these schemes are not secure. A more natural generalisation of Paillier's scheme to elliptic curves is given.

Note: This is the new version of the paper which was 2001/025 of the eprint archive. The new paper contains about twice as much information.

Metadata

Available format(s): PS
Category: Public-key cryptography
Publication info: Published elsewhere. To appear in J. Crypt
Keywords: Public key cryptography cryptanalysis elliptic
Contact author(s): steven @ cs bris ac uk
History: 2001-06-20: received
Short URL: https://ia.cr/2001/050
License: CC BY

BibTeX

@misc{cryptoeprint:2001/050,
      author = {Steven D Galbraith},
      title = {Elliptic curve Paillier schemes},
      howpublished = {Cryptology {ePrint} Archive, Paper 2001/050},
      year = {2001},
      url = {https://eprint.iacr.org/2001/050}
}