Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: EUROCRYPT 2003, pp. 416–432 (2003)
Hartung, G., Kaidel, B., Koch, A., Koch, J., Rupp, A.: Fault-tolerant aggregate signatures. In: Public-Key Cryptography - PKC 2016, pp. 331–356 (2016)
Idalino, T.B.: Using combinatorial group testing to solve integrity issues. Master’s thesis, Universidade Federal de Santa Catarina, Brazil (2015)
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)
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)
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). https://doi.org/10.1007/978-3-642-14785-2_12
Ma, D.: Practical forward secure sequential aggregate signatures. In: ASIACCS 2008, pp. 341–352. ACM (2008)
Macula, A.J.: A simple construction of d-disjunct matrices with certain constant weights. Discrete Math. 162(1), 311–312 (1996)
Mykletun, E., Narasimha, M., Tsudik, G.: Authentication and integrity in outsourced databases. ACM Trans. Storage 2, 107–138 (2006)
Porat, E., Rothschild, A.: Explicit nonadaptive combinatorial group testing schemes. IEEE Trans. Inf. Theory 57, 7982–7989 (2011)
Sperner, E.: Ein Satz über Untermengen einer endlichen Menge. Mathematische Zeitschrift 27, 544–548 (1928)
Wasef, A., Shen, X.: ASIC: aggregate signatures and certificates verification scheme for vehicular networks. In: GLOBECOM 2009, pp. 1–6 (2009)
Zaverucha, G.M., Stinson, D.R.: Group testing and batch verification. In: ICITS 2009, pp. 140–157 (2009)
Acknowledgments
Thais Bardini Idalino acknowledges funding granted from CNPq-Brazil [233697/2014-4]. Lucia Moura was supported by an NSERC discovery grant.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Bardini Idalino, T., Moura, L. (2018). Efficient Unbounded Fault-Tolerant Aggregate Signatures Using Nested Cover-Free Families. In: Iliopoulos, C., Leong, H., Sung, WK. (eds) Combinatorial Algorithms. IWOCA 2018. Lecture Notes in Computer Science(), vol 10979. Springer, Cham. https://doi.org/10.1007/978-3-319-94667-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-94667-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94666-5
Online ISBN: 978-3-319-94667-2
eBook Packages: Computer ScienceComputer Science (R0)