Efficient Unbounded Fault-Tolerant Aggregate Signatures Using Nested Cover-Free Families

  • Thais Bardini IdalinoEmail author
  • Lucia Moura
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10979)


Aggregate signatures are used to create one short proof of authenticity and integrity from a set of digital signatures. However, one invalid signature in the set invalidates the entire aggregate, giving no information on which signatures are valid. Hartung et al. (PKC 2016) proposed a fault-tolerant aggregate signature scheme based on combinatorial group testing. Given a bound d on the number of invalid signatures, the scheme can determine which signatures are invalid, and guarantees a moderate increase on the size of the aggregate signature when there is an upper bound on the number n of signatures to be aggregated. However, for the case of unbounded n the constructions provided had constant compression ratio, i.e. the signature size grew linearly with n. In this paper we propose a solution to the unbounded scheme with increasing compression ratio for every d. In particular, for \(d=1\) the compression ratio is the best possible and meets the information theoretical bound.


Aggregate signature Fault-tolerance Cover-free family Digital signature Combinatorial group testing 



Thais Bardini Idalino acknowledges funding granted from CNPq-Brazil [233697/2014-4]. Lucia Moura was supported by an NSERC discovery grant.


  1. 1.
    Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: EUROCRYPT 2003, pp. 416–432 (2003)Google Scholar
  2. 2.
    Hartung, G., Kaidel, B., Koch, A., Koch, J., Rupp, A.: Fault-tolerant aggregate signatures. In: Public-Key Cryptography - PKC 2016, pp. 331–356 (2016)CrossRefGoogle Scholar
  3. 3.
    Idalino, T.B.: Using combinatorial group testing to solve integrity issues. Master’s thesis, Universidade Federal de Santa Catarina, Brazil (2015)Google Scholar
  4. 4.
    Idalino, T.B., Moura, L., Custódio, R.F., Panario, D.: Locating modifications in signed data for partial data integrity. Inf. Process. Lett. 115(10), 731–737 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Li, P.C., van Rees, G.H.J., Wei, R.: Constructions of 2-cover-free families and related separating hash families. J. Comb. Des. 14(6), 423–440 (2006)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Li, Z., Gong, G.: Data aggregation integrity based on homomorphic primitives in sensor networks. In: Nikolaidis, I., Wu, K. (eds.) ADHOC-NOW 2010. LNCS, vol. 6288, pp. 149–162. Springer, Heidelberg (2010). Scholar
  7. 7.
    Ma, D.: Practical forward secure sequential aggregate signatures. In: ASIACCS 2008, pp. 341–352. ACM (2008)Google Scholar
  8. 8.
    Macula, A.J.: A simple construction of d-disjunct matrices with certain constant weights. Discrete Math. 162(1), 311–312 (1996)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mykletun, E., Narasimha, M., Tsudik, G.: Authentication and integrity in outsourced databases. ACM Trans. Storage 2, 107–138 (2006)CrossRefGoogle Scholar
  10. 10.
    Porat, E., Rothschild, A.: Explicit nonadaptive combinatorial group testing schemes. IEEE Trans. Inf. Theory 57, 7982–7989 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Sperner, E.: Ein Satz über Untermengen einer endlichen Menge. Mathematische Zeitschrift 27, 544–548 (1928)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Wasef, A., Shen, X.: ASIC: aggregate signatures and certificates verification scheme for vehicular networks. In: GLOBECOM 2009, pp. 1–6 (2009)Google Scholar
  13. 13.
    Zaverucha, G.M., Stinson, D.R.: Group testing and batch verification. In: ICITS 2009, pp. 140–157 (2009)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of OttawaOttawaCanada

Personalised recommendations