Abstract
We show that a strong notion of KDM security cannot be obtained by any encryption scheme in the auxiliary input setting, assuming Learning With Errors (LWE) and one-way permutations. The notion of security we deal with guarantees that for any (possibly inefficient) function f, it is computationally hard to distinguish between an encryption of \(\mathbf {0}\) and an encryption of \(f(\mathsf {pk}, z)\), where \(\mathsf {pk} \) is the public key and z is the auxiliary input. Furthermore, we show that this holds even when restricted to bounded-length auxiliary input where z is much shorter than \(\mathsf {pk} \) under the additional assumption that (non-leveled) fully homomorphic encryption exists.
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
References
Barak, B., et al.: On the (im)possibility of obfuscating programs. J. ACM 59(2), 6:1–6:48 (2012)
Bellare, M., Stepanovs, I., Tessaro, S.: Contention in cryptoland: obfuscation, leakage and UCE. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 542–564. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49099-0_20
Black, J., Rogaway, P., Shrimpton, T.: Encryption-scheme security in the presence of key-dependent messages. In: Nyberg, K., Heys, H. (eds.) SAC 2002. LNCS, vol. 2595, pp. 62–75. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36492-7_6
Brzuska, C., Mittelbach, A.: Indistinguishability obfuscation versus multi-bit point obfuscation with auxiliary input. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 142–161. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45608-8_8
Canetti, R., Chen, Y., Reyzin, L., Rothblum, R.D.: Fiat-Shamir and correlation intractability from strong KDM-secure encryption. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 91–122. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78381-9_4
Canetti, R., Tauman Kalai, Y., Varia, M., Wichs, D.: On symmetric encryption and point obfuscation. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 52–71. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11799-2_4
Deshpande, A., Kalai, Y.: Proofs of ignorance and applications to 2-message witness hiding. IACR Cryptology ePrint Archive 2018/896 (2018). version dated: 25-Sept- 2018
Deshpande, A., Kalai, Y.: Proofs of ignorance and applications to 2-message witness hiding. IACR Cryptology ePrint Archive 2018/896 (2018). version dated: 02-Mar-2019
Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_5
Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: STOC, pp. 25–32. ACM (1989)
Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)
Goyal, R., Koppula, V., Waters, B.: Lockable obfuscation. In: 58th IEEE Annual Symposium on Foundations of Computer Science (FOCS), pp. 612–621 (2017)
Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)
Hsiao, C.-Y., Lu, C.-J., Reyzin, L.: Conditional computational entropy, or toward separating pseudoentropy from compressibility. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 169–186. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72540-4_10
Komargodski, I., Moran, T., Naor, M., Pass, R., Rosen, A., Yogev, E.: One-way functions and (im)perfect obfuscation. In: 55th IEEE Annual Symposium on Foundations of Computer Science (FOCS), pp. 374–383 (2014)
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC, pp. 84–93. ACM (2005)
Wichs, D., Zirdelis, G.: Obfuscating compute-and-compare programs under LWE. In: 58th IEEE Annual Symposium on Foundations of Computer Science (FOCS), pp. 600–611 (2017)
Acknowledgements
This work was supported in part by NSF Award SATC-1704788, NSF Award RI-1703846, AFOSR Award FA9550-18-1-0267, and by NSF Award DGE-1650441. This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2019-19-020700006. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Freitag, C., Komargodski, I., Pass, R. (2020). Impossibility of Strong KDM Security with Auxiliary Input. In: Galdi, C., Kolesnikov, V. (eds) Security and Cryptography for Networks. SCN 2020. Lecture Notes in Computer Science(), vol 12238. Springer, Cham. https://doi.org/10.1007/978-3-030-57990-6_25
Download citation
DOI: https://doi.org/10.1007/978-3-030-57990-6_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-57989-0
Online ISBN: 978-3-030-57990-6
eBook Packages: Computer ScienceComputer Science (R0)