Anonymity on Paillier's trap-door permutation

Authors:
Ryotaro Hayashi;Keisuke Tanaka
Affiliations:
TOSHIBA Corporation, Kawasaki-shi, Kanagawa, Japan;Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan
Venue:
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Year:
2007

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Abstract

It is said that an encryption scheme provides anonymity when it is infeasible for the adversary to determine under which key the ciphertext was created. (i.e. the receiver of the ciphertext is anonymous from the point of view of the adversary.) From the previous results, we can find four techniques, repeating, expanding, RSACD, and sampling twice, for achieving the anonymity property of the encryption schemes based on RSA. In this paper, we focus on the four techniques described above in the case using Paillier's bijective function instead of the RSA function. We slightly modify his function and construct a family of Paillier's trapdoor permutations, and a family of Paillier's trap-door permutations with a common domain. We also apply our proposed families of Paillier's trapdoor permutations to encryption with the above four techniques, and prove their security.