An Improvement for Fully Homomorphic Encryption over Integers with Shorter Public Keys

Abstract:

This paper puts forward a more efficient fully homomorphic encryption scheme with a view to improving the oversized public key based on the Dijk’s scheme.Encrypted with a cubic form in the public key elements instead of quadratic form by adopting Gentry’s fully homomorphic techonology.The results show that the public key size reduce from to compared to the Coron’s scheme.The security of the proposed scheme is based on both the approximate GCD problem and the sparse-subset sum problem.

• Periodical: Advanced Materials Research (Volumes 989-994)
• Pages: 4326-4331
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.989-994.4326
• Online since: July 2014
• Authors: Ze Tao Jiang*, Xiao Te Huang
• Keywords: Approximate GCD, Fully Homomorphic Encryption, Public Key Size, Sparse Subset Sum Problem

References

[1] Rivest R L, Adleman L, Dertouzos M L. On data banks and privacy homomorphisms[Z]. Foundations of Secure Computation, (1978).

[2] Lipton B. Searching for Elements in Black Box Fields and Applications[C]/Proc. of Cryptology-Crypo'96. [S.I. ]: Springer-Verlag, 1996: 283-297.

[3] Domingo-Ferrer J. A Provably Secure Additive and Multiplicative Privacy Homomorphism [C]/Proc. of the 5th International Conference on Information Security. [S. l. ]: Springer- Verlag, 2002: 471-483.

DOI: 10.1007/3-540-45811-5_37

[4] Brickell E F, Yacobi Y. On Privacy Homomorphisms[C]/Proc. of Cryptology-Euro Crypt'87. Berlin, Germany: Springer-Verlag, 1987: 117-126.

[5] Feigenbaum J, Merritt M. Open Question, Talk Abstracts, and Summary of Discussions [EB/OL]. (1991-12-05).

[6] Fellows M, Koblitz N. Combinatorial Cryptosystems Galore![Z]. (1993).

[7] C. Gentry. Fully homomorphic encryption using ideal lattices. In STOC'09, pages 169-178. ACM, (2009).

[8] C. Gentry, A fully homomorphic encryption scheme. Ph.D. thesis, Stanford University, 2009. Available at http: /crypto. stanford. edu/craig.

[9] M. van Dijk,C. Gentry,S. Halevi and V. Vaikuntanathan, Fully homomorphic encryption over the integers. In H. Gilbert(Ed. ), EUROCRYPT 2010, LNCS, vol. 6110, Springer, 2010, pp.24-43.

DOI: 10.1007/978-3-642-13190-5_2

[10] C. Gentry and S. Halevi. Implementing Gentry's fully homomorphic encryption scheme. In K. Paterson(Ed. ), EUROCRYPT 2011, LNCS, Springer, (2011).

DOI: 10.1007/978-3-642-20465-4_9

[11] D. Stehle and R. Steinfeld, Faster fully homomorphic encryption. In M. Abe(Ed. ), ASIACRYPT 2010, LNCS, vol. 6477, Springer, 2010, pp.377-394.

DOI: 10.1007/978-3-642-17373-8_22

[12] Nigel P. Smart and Frederik Vercauteren. Fully homomorphic encryption with relatively small key and ciphertext sizes. In Public Key Cryptography-PKC'10, volume 6056 of Lecture Notes in Computer Science, pages 420-443. Springer, (2010).

DOI: 10.1007/978-3-642-13013-7_25

[13] J.S. Coron,A. Mandal,D. Naccache and M. Tibouchi, Fully Homomorphic Encryption over the Integers with Shorter Public Keys. In P. Rogaway(Ed. ), CRYPTO 2011, LNCS, vol. 6841, Springer, 2011, pp.487-504. Full version available at IACR eprint.

DOI: 10.1007/978-3-642-22792-9_28