Paper 2018/640

Lower Bounds on Structure-Preserving Signatures for Bilateral Messages

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


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.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. MINOR revision.Conference on Security and Cryptography for Networks (SCN 2018)
Structure-Preserving SignaturesBilateral MessagesCrucial Relation
Contact author(s)
miguel ambrona @ imdea org
2018-07-06: received
Short URL
Creative Commons Attribution


      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},
      note = {\url{}},
      url = {}
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