Abstract
We propose a general framework that converts (ordinary) signature schemes having certain properties into linearly homomorphic signature schemes, i.e., schemes that allow authentication of linear functions on signed data. The security of the homomorphic scheme follows from the same computational assumption as is used to prove security of the underlying signature scheme. We show that the following signature schemes have the required properties and thus give rise to secure homomorphic signatures in the standard model:
-
The scheme of Waters (Eurocrypt 2005), secure under the computational Diffie-Hellman asumption in bilinear groups.
-
The scheme of Boneh and Boyen (Eurocrypt 2004, J. Cryptology 2008), secure under the q-strong Diffie-Hellman assumption in bilinear groups.
-
The scheme of Gennaro, Halevi, and Rabin (Eurocrypt 1999), secure under the strong RSA assumption.
-
The scheme of Hohenberger and Waters (Crypto 2009), secure under the RSA assumption.
Our systems not only allow weaker security assumptions than were previously available for homomorphic signatures in the standard model, but also are secure in a model that allows a stronger adversary than in other proposed schemes.
Our framework also leads to efficient linearly homomorphic signatures that are secure against our stronger adversary under weak assumptions (CDH or RSA) in the random oracle model; all previous proofs of security in the random oracle model break down completely when faced with our stronger adversary.
Chapter PDF
Similar content being viewed by others
References
Ahlswede, R., Cai, N., Li, S., Yeung, R.: Network information flow. IEEE Transactions on Information Theory 46(4), 1204–1216 (2000)
Attrapadung, N., Libert, B.: Homomorphic Network Coding Signatures in the Standard Model. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 17–34. Springer, Heidelberg (2011)
Boneh, D., Boyen, X.: Efficient Selective-ID Secure Identity-Based Encryption Without Random Oracles. In: Cachin, C., Camenisch, J. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)
Boneh, D., Boyen, X.: Short signatures without random oracles and the SDH assumption in bilinear groups. J. Cryptology 21, 149–177 (2008); extended abstract in Advances in Cryptology — EUROCRYPT 2004
Boneh, D., Freeman, D., Katz, J., Waters, B.: Signing a Linear Subspace: Signature Schemes for Network Coding. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 68–87. Springer, Heidelberg (2009)
Boneh, D., Freeman, D.M.: Homomorphic Signatures for Polynomial Functions. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 149–168. Springer, Heidelberg (2011), full version available at http://eprint.iacr.org/2011/018
Boneh, D., Freeman, D.M.: Linearly Homomorphic Signatures over Binary Fields and New Tools for Lattice-Based Signatures. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 1–16. Springer, Heidelberg (2011), Full version available at http://eprint.iacr.org/2010/453
Catalano, D., Fiore, D., Warinschi, B.: Adaptive Pseudo-free Groups and Applications. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 207–223. Springer, Heidelberg (2011)
Catalano, D., Fiore, D., Warinschi, B.: Efficient Network Coding Signatures in the Standard Model. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 680–696. Springer, Heidelberg (2012), http://eprint.iacr.org/2011/696
Charles, D., Jain, K., Lauter, K.: Signatures for network coding. International Journal of Information and Coding Theory 1(1), 3–14 (2009)
Fischlin, M.: The Cramer-Shoup Strong-RSA Signature Scheme Revisited. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 116–129. Springer, Heidelberg (2002)
Freeman, D.M.: Improved security for linearly homomorphic signatures: A generic framework. Cryptology ePrint Archive, Report 2012/060 (2012), http://eprint.iacr.org/2012/060
Gennaro, R., Halevi, S., Rabin, T.: Secure Hash-and-Sign Signatures without the Random Oracle. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 123–139. Springer, Heidelberg (1999)
Gennaro, R., Katz, J., Krawczyk, H., Rabin, T.: Secure Network Coding over the Integers. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 142–160. Springer, Heidelberg (2010)
Gentry, C., Silverberg, A.: Hierarchical ID-Based Cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002)
Hofheinz, D., Kiltz, E.: Programmable Hash Functions and Their Applications. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 21–38. Springer, Heidelberg (2008)
Hohenberger, S., Waters, B.: Realizing Hash-and-Sign Signatures under Standard Assumptions. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 333–350. Springer, Heidelberg (2009)
Hohenberger, S., Waters, B.: Short and Stateless Signatures from the RSA Assumption. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 654–670. Springer, Heidelberg (2009)
Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic Signature Schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 244–262. Springer, Heidelberg (2002)
Krawczyk, H., Rabin, T.: Chameleon signatures. In: Network and Distributed System Security Symposium (2000)
Krohn, M., Freedman, M., Mazières, D.: On-the-fly verification of rateless erasure codes for efficient content distribution. In: Proc. of IEEE Symposium on Security and Privacy, pp. 226–240 (2004)
Lewko, A.B., Waters, B.: New Techniques for Dual System Encryption and Fully Secure HIBE with Short Ciphertexts. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 455–479. Springer, Heidelberg (2010)
Li, S.-Y.R., Yeung, R.W., Cai, N.: Linear network coding. IEEE Trans. Info. Theory 49(2), 371–381 (2003)
Waters, B.: Efficient Identity-Based Encryption Without Random Oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 320–329. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 International Association for Cryptologic Research
About this paper
Cite this paper
Freeman, D.M. (2012). Improved Security for Linearly Homomorphic Signatures: A Generic Framework. In: Fischlin, M., Buchmann, J., Manulis, M. (eds) Public Key Cryptography – PKC 2012. PKC 2012. Lecture Notes in Computer Science, vol 7293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30057-8_41
Download citation
DOI: https://doi.org/10.1007/978-3-642-30057-8_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30056-1
Online ISBN: 978-3-642-30057-8
eBook Packages: Computer ScienceComputer Science (R0)Springer Nature Proceedings Computer Science