Abstract
Following Gentry’s breakthrough work [7], there is currently great interest on fully-homomorphic encryption (FHE), which allows to compute arbitrary functions on encrypted data. Though the area has seen much progress recently (such as [10,11,5,2,1,8,6]), it is still unknown if fully-homomorphic encryption will ever become truly practical one day, or if it will remain a theoretical curiosity. In order to find out, several FHE numerical challenges have been proposed by Gentry and Halevi [9], and by Coron et al. [5], which provide concrete parameters whose efficiency and security can be studied. We report on recent attempts [3,4] at breaking FHE challenges, and we discuss the difficulties of assessing precisely the security level of FHE challenges, based on the state-of-the-art. It turns out that security estimates were either missing or too optimistic.
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Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. Cryptology ePrint Archive, Report 2011/344 (2011), http://eprint.iacr.org/
Brakerski, Z., Vaikuntanathan, V.: Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505–524. Springer, Heidelberg (2011)
Chen, Y., Nguyen, P.Q.: BKZ 2.0: Better Lattice Security Estimates. In: Lee, D.H. (ed.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 1–20. Springer, Heidelberg (2011)
Chen, Y., Nguyen, P.Q.: Faster algorithms for approximate common divisors: Breaking fully-homomorphic-encryption challenges over the integers. Cryptology ePrint Archive, Report 2011/436 (2011), http://eprint.iacr.org/
Coron, J.-S., Mandal, A., Naccache, D., Tibouchi, M.: Fully Homomorphic Encryption over the Integers with Shorter Public-Keys. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 487–504. Springer, Heidelberg (2011)
Coron, J.-S., Naccache, D., Tibouchi, M.: Optimization of fully homomorphic encryption. Cryptology ePrint Archive, Report 2011/440 (2011), http://eprint.iacr.org/
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proc. STOC 2009, pp. 169–178. ACM (2009)
Gentry, C., Halevi, S.: Fully homomorphic encryption without squashing using depth-3 arithmetic circuits. Cryptology ePrint Archive, Report 2011/279 (2011), http://eprint.iacr.org/
Gentry, C., Halevi, S.: Implementing Gentry’s Fully-Homomorphic Encryption Scheme. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 129–148. Springer, Heidelberg (2011)
Smart, N.P., Vercauteren, F.: Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 420–443. Springer, Heidelberg (2010)
van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully Homomorphic Encryption over the Integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010)
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Nguyen, P.Q. (2011). Breaking Fully-Homomorphic-Encryption Challenges. In: Lin, D., Tsudik, G., Wang, X. (eds) Cryptology and Network Security. CANS 2011. Lecture Notes in Computer Science, vol 7092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25513-7_2
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DOI: https://doi.org/10.1007/978-3-642-25513-7_2
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