Lower Bounds on Structure-Preserving Signatures for Bilateral Messages

Masayuki Abe; Miguel Ambrona; Miyako Ohkubo; Mehdi Tibouchi

Paper 2018/640

Lower Bounds on Structure-Preserving Signatures for Bilateral Messages

Masayuki Abe, Miguel Ambrona, Miyako Ohkubo, and Mehdi Tibouchi

Abstract

Lower bounds for structure-preserving signature (SPS) schemes based on non-interactive assumptions have only been established in the case of unilateral messages, i.e. schemes signing tuples of group elements all from the same source group. In this paper, we consider the case of bilateral messages, consisting of elements from both source groups. We show that, for Type-III bilinear groups, SPS’s must consist of at least 6 group elements: many more than the 4 elements needed in the unilateral case, and optimal, as it matches a known upper bound from the literature. We also obtain the first non-trivial lower bounds for SPS’s in Type-II groups: a minimum of 4 group elements, whereas constructions with 3 group elements are known from interactive assumptions.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. Conference on Security and Cryptography for Networks (SCN 2018)
Keywords: Structure-Preserving Signatures Bilateral Messages Crucial Relation
Contact author(s): miguel ambrona @ imdea org
History: 2018-07-06: received
Short URL: https://ia.cr/2018/640
License: CC BY

BibTeX

@misc{cryptoeprint:2018/640,
      author = {Masayuki Abe and Miguel Ambrona and Miyako Ohkubo and Mehdi Tibouchi},
      title = {Lower Bounds on Structure-Preserving Signatures for Bilateral Messages},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/640},
      year = {2018},
      url = {https://eprint.iacr.org/2018/640}
}