Abstract
Robustness is a notion often tacitly assumed while working with encrypted data. Roughly speaking, it states that a ciphertext cannot be decrypted under different keys. Initially formalized in a public-key context, it has been further extended to key-encapsulation mechanisms, and more recently to pseudorandom functions, message-authentication codes and authenticated encryption. In this work, we motivate the importance of establishing similar guarantees for functional encryption schemes, even under adversarially generated keys. Our main security notion is intended to capture the scenario where a ciphertext obtained under a master key (corresponding to Authority 1) is decrypted by functional keys issued under a different master key (Authority 2). Furthermore, we show there exist simple functional encryption schemes where robustness under adversarial key-generation is not achieved. As a secondary and independent result, we formalize robustness for digital signatures – a signature should not verify under multiple keys – and point out that certain signature schemes are not robust when the keys are adversarially generated.
We present simple, generic transforms that turn a scheme into a robust one, while maintaining the original scheme’s security. For the case of public-key functional encryption, we look into ciphertext anonymity and provide a transform achieving it.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
There are several scenarios leading to such corruption, including memory corruption.
- 2.
We may assume that malformed keys would be easily recognisable and rejected.
- 3.
See for instance [5] for the definition and usage of a cryptographic pairing.
- 4.
\(\mathsf {sk}\) is common to all users querying a \({\mathsf {sk}_f}\).
References
Abdalla, M., Bellare, M., Neven, G.: Robust encryption. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 480–497. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11799-2_28
Abdalla, M., Bourse, F., De Caro, A., Pointcheval, D.: Simple functional encryption schemes for inner products. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 733–751. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46447-2_33
Agrawal, S., Libert, B., Stehlé, D.: Fully secure functional encryption for inner products, from standard assumptions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 333–362. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53015-3_12
Boneh, D., Boyen, X.: Short signatures without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_4
Boneh, D., Boyen, X.: Short signatures without random oracles and the SDH assumption in bilinear groups. J. Cryptol. 21(2), 149–177 (2008)
Boneh, D., Sahai, A., Waters, B.: Functional encryption: definitions and challenges. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 253–273. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19571-6_16
Boyle, E., Goldwasser, S., Ivan, I.: Functional signatures and pseudorandom functions. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 501–519. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_29
Brakerski, Z., Komargodski, I., Segev, G.: Multi-input functional encryption in the private-key setting: stronger security from weaker assumptions. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 852–880. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_30
Chou, T., Orlandi, C.: The simplest protocol for oblivious transfer. In: Lauter, K., Rodríguez-Henríquez, F. (eds.) LATINCRYPT 2015. LNCS, vol. 9230, pp. 40–58. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22174-8_3
Cohen, A., Holmgren, J., Nishimaki, R., Vaikuntanathan, V., Wichs, D.: Watermarking cryptographic capabilities. In: Wichs, D., Mansour, Y. (eds.) 48th ACM STOC, pp. 1115–1127. ACM Press, June 2016
Damgård, I.B.: Collision free hash functions and public key signature schemes. In: Chaum, D., Price, W.L. (eds.) EUROCRYPT 1987. LNCS, vol. 304, pp. 203–216. Springer, Heidelberg (1988). https://doi.org/10.1007/3-540-39118-5_19
Farshim, P., Libert, B., Paterson, K.G., Quaglia, E.A.: Robust encryption, revisited. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 352–368. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_22
Farshim, P., Orlandi, C., Roşie, R.: Security of symmetric primitives under incorrect usage of keys. IACR Trans. Symm. Cryptol. 2017(1), 449–473 (2017)
Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM 33(4), 792–807 (1986)
Goldwasser, S., Micali, S., Rivest, R.L.: A “Paradoxical” solution to the signature problem. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, p. 467. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_37
Grubbs, P., Lu, J., Ristenpart, T.: Message franking via committing authenticated encryption. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10403, pp. 66–97. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63697-9_3
Jarecki, S., Krawczyk, H., Xu, J.: OPAQUE: an asymmetric PAKE protocol secure against pre-computation attacks. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 456–486. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_15
Komargodski, I., Segev, G.: From minicrypt to obfustopia via private-key functional encryption. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 122–151. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56620-7_5
Mohassel, P.: A closer look at anonymity and robustness in encryption schemes. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 501–518. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_29
O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive, Report 2010/556 (2010). http://eprint.iacr.org/2010/556
Yao, A.C.-C.: Theory and applications of trapdoor functions (extended abstract). In: 23rd FOCS, pp. 80–91. IEEE Computer Society Press, November 1982
Acknowledgements
The authors thank to anonymous reviewers for valuable comments. Roşie was supported by EU Horizon 2020 research and innovation programme under grant agreements No H2020-ERC-2017-ADG-787390 CLOUDMAP and No H2020-MSCA-ITN-2014-643161 ECRYPT-NET.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Géraud, R., Naccache, D., Roşie, R. (2019). Robust Encryption, Extended. In: Matsui, M. (eds) Topics in Cryptology – CT-RSA 2019. CT-RSA 2019. Lecture Notes in Computer Science(), vol 11405. Springer, Cham. https://doi.org/10.1007/978-3-030-12612-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-12612-4_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-12611-7
Online ISBN: 978-3-030-12612-4
eBook Packages: Computer ScienceComputer Science (R0)