---
_id: '1592'
abstract:
- lang: eng
  text: A modular approach to constructing cryptographic protocols leads to simple
    designs but often inefficient instantiations. On the other hand, ad hoc constructions
    may yield efficient protocols at the cost of losing conceptual simplicity. We
    suggest a new design paradigm, structure-preserving cryptography, that provides
    a way to construct modular protocols with reasonable efficiency while retaining
    conceptual simplicity. A cryptographic scheme over a bilinear group is called
    structure-preserving if its public inputs and outputs consist of elements from
    the bilinear groups and their consistency can be verified by evaluating pairing-product
    equations. As structure-preserving schemes smoothly interoperate with each other,
    they are useful as building blocks in modular design of cryptographic applications.
    This paper introduces structure-preserving commitment and signature schemes over
    bilinear groups with several desirable properties. The commitment schemes include
    homomorphic, trapdoor and length-reducing commitments to group elements, and the
    structure-preserving signature schemes are the first ones that yield constant-size
    signatures on multiple group elements. A structure-preserving signature scheme
    is called automorphic if the public keys lie in the message space, which cannot
    be achieved by compressing inputs via a cryptographic hash function, as this would
    destroy the mathematical structure we are trying to preserve. Automorphic signatures
    can be used for building certification chains underlying privacy-preserving protocols.
    Among a vast number of applications of structure-preserving protocols, we present
    an efficient round-optimal blind-signature scheme and a group signature scheme
    with an efficient and concurrently secure protocol for enrolling new members.
acknowledgement: The authors would like to thank the anonymous reviewers of this paper.
  We also would like to express our appreciation to the program committee and the
  anonymous reviewers for CRYPTO 2010. The first author thanks Sherman S. M. Chow
  for his comment on group signatures in Sect. 7.1.
article_processing_charge: No
author:
- first_name: Masayuki
  full_name: Abe, Masayuki
  last_name: Abe
- first_name: Georg
  full_name: Fuchsbauer, Georg
  id: 46B4C3EE-F248-11E8-B48F-1D18A9856A87
  last_name: Fuchsbauer
- first_name: Jens
  full_name: Groth, Jens
  last_name: Groth
- first_name: Kristiyan
  full_name: Haralambiev, Kristiyan
  last_name: Haralambiev
- first_name: Miyako
  full_name: Ohkubo, Miyako
  last_name: Ohkubo
citation:
  ama: Abe M, Fuchsbauer G, Groth J, Haralambiev K, Ohkubo M. Structure preserving
    signatures and commitments to group elements. <i>Journal of Cryptology</i>. 2016;29(2):363-421.
    doi:<a href="https://doi.org/10.1007/s00145-014-9196-7">10.1007/s00145-014-9196-7</a>
  apa: Abe, M., Fuchsbauer, G., Groth, J., Haralambiev, K., &#38; Ohkubo, M. (2016).
    Structure preserving signatures and commitments to group elements. <i>Journal
    of Cryptology</i>. Springer. <a href="https://doi.org/10.1007/s00145-014-9196-7">https://doi.org/10.1007/s00145-014-9196-7</a>
  chicago: Abe, Masayuki, Georg Fuchsbauer, Jens Groth, Kristiyan Haralambiev, and
    Miyako Ohkubo. “Structure Preserving Signatures and Commitments to Group Elements.”
    <i>Journal of Cryptology</i>. Springer, 2016. <a href="https://doi.org/10.1007/s00145-014-9196-7">https://doi.org/10.1007/s00145-014-9196-7</a>.
  ieee: M. Abe, G. Fuchsbauer, J. Groth, K. Haralambiev, and M. Ohkubo, “Structure
    preserving signatures and commitments to group elements,” <i>Journal of Cryptology</i>,
    vol. 29, no. 2. Springer, pp. 363–421, 2016.
  ista: Abe M, Fuchsbauer G, Groth J, Haralambiev K, Ohkubo M. 2016. Structure preserving
    signatures and commitments to group elements. Journal of Cryptology. 29(2), 363–421.
  mla: Abe, Masayuki, et al. “Structure Preserving Signatures and Commitments to Group
    Elements.” <i>Journal of Cryptology</i>, vol. 29, no. 2, Springer, 2016, pp. 363–421,
    doi:<a href="https://doi.org/10.1007/s00145-014-9196-7">10.1007/s00145-014-9196-7</a>.
  short: M. Abe, G. Fuchsbauer, J. Groth, K. Haralambiev, M. Ohkubo, Journal of Cryptology
    29 (2016) 363–421.
date_created: 2018-12-11T11:52:54Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2025-09-18T11:02:49Z
day: '01'
department:
- _id: KrPi
doi: 10.1007/s00145-014-9196-7
external_id:
  isi:
  - '000371077900004'
intvolume: '        29'
isi: 1
issue: '2'
language:
- iso: eng
month: '04'
oa_version: None
page: 363 - 421
publication: Journal of Cryptology
publication_status: published
publisher: Springer
publist_id: '5579'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Structure preserving signatures and commitments to group elements
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 29
year: '2016'
...