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.
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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.
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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
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DOI: https://doi.org/10.1007/978-3-319-94667-2_5
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