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Lower Bounds on Structure-Preserving Signatures for Bilateral Messages

  • Masayuki AbeEmail author
  • Miguel Ambrona
  • Miyako Ohkubo
  • Mehdi Tibouchi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11035)

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.

Keywords

Structure-preserving signatures Bilateral messages Crucial relation 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Masayuki Abe
    • 1
    Email author
  • Miguel Ambrona
    • 2
  • Miyako Ohkubo
    • 3
  • Mehdi Tibouchi
    • 1
  1. 1.Secure Platform LaboratoriesNTT CorporationTokyoJapan
  2. 2.IMDEA Software Institute & Universidad Politécnica de MadridMadridSpain
  3. 3.Security Fundamentals LabCSRI, NICTTokyoJapan

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