Abstract
In this work the first linearly homomorphic authenticated encryption scheme with public verifiability and provable correctness, called \(\mathsf {LEPCoV}\), is presented. It improves the initial proposal by avoiding false negatives during the verification algorithm. This work provides a detailed description of \(\mathsf {LEPCoV}\), a comparison with the original scheme, a security and correctness proof, and a performance analysis showing that all algorithms run in reasonable time for parameters that are currently considered secure. The scheme presented here allows a user to outsource computations on encrypted data to the cloud, such that any third party can verify the correctness of the computations without having access to the original data. This makes this work an important contribution to cloud computing and applications where operations on sensitive data have to be performed, such as statistics on medical records and tallying of electronically cast votes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
An, J.H., Bellare, M.: Does encryption with redundancy provide authenticity? In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 512–528. Springer, Heidelberg (2001). doi:10.1007/3-540-44987-6_31
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). doi:10.1007/978-3-642-19379-8_2
Attrapadung, N., Libert, B., Peters, T.: Computing on authenticated data: new privacy definitions and constructions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 367–385. Springer, Heidelberg (2012). doi:10.1007/978-3-642-34961-4_23
Attrapadung, N., Libert, B., Peters, T.: Efficient completely context-hiding quotable and linearly homomorphic signatures. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 386–404. Springer, Heidelberg (2013). doi:10.1007/978-3-642-36362-7_24
Bellare, M., Namprempre, C.: Authenticated encryption: relations among notions and analysis of the generic composition paradigm. J. Crypt. 21(4), 469–491 (2008)
Benaloh, J.: Dense probabilistic encryption. In: Proceedings of the Workshop on Selected Areas of Cryptography, pp. 120–128 (1994)
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). doi:10.1007/978-3-642-00468-1_5
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). doi:10.1007/978-3-642-20465-4_10
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). doi:10.1007/978-3-642-19379-8_1
Catalano, D., Fiore, D., Gennaro, R., Vamvourellis, K.: Algebraic (trapdoor) one-way functions and their applications. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 680–699. Springer, Heidelberg (2013). doi:10.1007/978-3-642-36594-2_38
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). doi:10.1007/978-3-642-30057-8_40
Catalano, D., Marcedone, A., Puglisi, O.: Authenticating computation on groups: new homomorphic primitives and applications. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 193–212. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45608-8_11
Desmedt, Y.: Computer security by redefining what a computer is. In: Proceedings on the 1992–1993 Workshop on New security paradigms, pp. 160–166. ACM (1993)
ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985). doi:10.1007/3-540-39568-7_2
Freeman, D.M.: Improved security for linearly homomorphic signatures: a generic framework. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 697–714. Springer, Heidelberg (2012). doi:10.1007/978-3-642-30057-8_41
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). doi:10.1007/978-3-642-13013-7_9
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). doi:10.1007/3-540-45760-7_17
Joo, C., Yun, A.: Homomorphic authenticated encryption secure against chosen-ciphertext attack. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 173–192. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45608-8_10
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999). doi:10.1007/3-540-48910-X_16
Acknowledgments
This work has been co-funded by the DFG as part of project “Long-Term Secure Archiving” within the CRC 1119 CROSSING. In addition, it has received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 644962.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Struck, P., Schabhüser, L., Demirel, D., Buchmann, J. (2017). Linearly Homomorphic Authenticated Encryption with Provable Correctness and Public Verifiability. In: El Hajji, S., Nitaj, A., Souidi, E. (eds) Codes, Cryptology and Information Security. C2SI 2017. Lecture Notes in Computer Science(), vol 10194. Springer, Cham. https://doi.org/10.1007/978-3-319-55589-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-55589-8_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-55588-1
Online ISBN: 978-3-319-55589-8
eBook Packages: Computer ScienceComputer Science (R0)