Fully homomorphic encryption using hidden ideal lattice

IEEE Transactions on Information Forensics and Security

Volumn 8, Issue 12, 2013, Pages 2127-2137

  Plantard, Thomas ^a   Susilo, Willy ^a   Zhang, Zhenfei ^a  

^a UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

approximate greatest common divisor; bounded distance decoding problem; fully homomorphic encryption; Hidden lattice; ideal lattice

Indexed keywords

APPROXIMATE GREATEST COMMON DIVISORS; BOUNDED DISTANCE DECODING; FULLY HOMOMORPHIC ENCRYPTION; HIDDEN LATTICE; IDEAL LATTICE;

DECODING;

CRYPTOGRAPHY;

EID: 84888634213     PISSN: 15566013     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIFS.2013.2287732     Document Type: Article

References (33)

1. Z. Brakerski, C. Gentry, and V. Vaikuntanathan, "(Leveled) fully homomorphic encryption without bootstrapping," in Proc. 3rd ITCS, 2012, pp. 309-325.
2. Z. Brakerski and V. Vaikuntanathan, "Efficient fully homomorphic encryption from (standard) LWE," in Proc. IEEE 52nd FOCS, Oct. 2011, pp. 97-106.
3. Z. Brakerski and V. Vaikuntanathan, "Fully homomorphic encryption from ring-LWE and security for key dependent messages," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 6841, P. Rogaway, Ed. New York, NY, USA: Springer-Verlag, 2011, pp. 505-524.
4. Y. Chen and P. Q. Nguyen, "BKZ 2.0: Better lattice security estimates," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 7073, D. H. Lee and X. Wang, Eds. New York, NY, USA: Springer-Verlag, 2011, pp. 1-20.
5. Y. Chen and P. Q. Nguyen, "Faster algorithms for approximate common divisors: Breaking fully-homomorphic-encryption challenges over the integers," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 7237, D. Pointcheval and T. Johansson, Eds. New York, NY, USA: Springer-Verlag, 2012, pp. 502-519.
6. J.-S. Coron, A. Mandal, D. Naccache, and M. Tibouchi, "Fully homomorphic encryption over the integers with shorter public keys," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 6841, P. Rogaway, Ed. New York, NY, USA: Springer-Verlag, 2011, pp. 487-504.
7. J.-S. Coron, D. Naccache, and M. Tibouchi, "Public key compression and modulus switching for fully homomorphic encryption over the integers," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 7237, D. Pointcheval and T. Johansson, Eds. New York, NY, USA: Springer-Verlag, 2012, pp. 446-464.
8. C. Gentry, "Fully homomorphic encryption using ideal lattices," in Proc. STOC, 2009, pp. 169-178.
9. C. Gentry, "A fully homomorphic encyrption scheme," Ph.D. dissertation, Stanford Comput. Sci. Dept., Stanford Univ., Stanford, CA, USA, Sep. 2009.
10. C. Gentry, "Computing arbitrary functions of encrypted data," Commun. ACM, vol. 53, no. 3, pp. 97-105, 2010.
11. C. Gentry, "Toward basing fully homomorphic encryption on worstcase hardness," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 6223, T. Rabin, Ed. New York, NY, USA: Springer-Verlag, 2010, pp. 116-137.
12. C. Gentry and S. Halevi, "Implementing Gentry's fully-homomorphic encryption scheme," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 6632, K. G. Paterson, Ed. New York, NY, USA: Springer-Verlag, 2011, pp. 129-148.
13. C. Gentry, S. Halevi, C. Peikert, and N. P. Smart, "Ring switching in BGV-style homomorphic encryption," in Security and Cryptography for Networks (Lecture Notes in Computer Science), vol. 7485, I. Visconti and R. D. Prisco, Eds. New York, NY, USA: Springer-Verlag, 2012, pp. 19-37.
14. C. Gentry, S. Halevi, and N. P. Smart, "Better bootstrapping in fully homomorphic encryption," in Public Key Cryptography (Lecture Notes in Computer Science), vol. 7293, M. Fischlin, J. Buchmann, and M. Manulis, Eds. New York, NY, USA: Springer-Verlag, 2012, pp. 1-16.
15. C. Gentry, S. Halevi, and N. P. Smart, "Fully homomorphic encryption with polylog overhead," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 7237, D. Pointcheval and T. Johansson, Eds. New York, NY, USA: Springer-Verlag, 2012, pp. 465-482.
16. O. Goldreich, S. Goldwasser, and S. Halevi, "Public-key cryptosystems from lattice reduction problems," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 1294, B. S. Kaliski, Jr., Ed. New York, NY, USA: Springer-Verlag, 1997, pp. 112-131. (Pubitemid 127112548)
17. S. Goldwasser and S. Micali, "Probabilistic encryption," J. Comput. Syst. Sci., vol. 28, no. 2, pp. 270-299, 1984.
18. G. H. Golub and C. F. van Loan, Matrix Computations, 3rd ed. Baltimore, MD, USA: The Johns Hopkins Univ. Press, 1996.
19. N. Howgrave-Graham, "Approximate integer common divisors," in Cryptography and Lattices (Lecture Notes in Computer Science), vol. 2146, J. H. Silverman, Ed. New York, NY, USA: Springer-Verlag, 2001, pp. 51-66. (Pubitemid 33329086)
20. Y.-K. Liu, V. Lyubashevsky, and D. Micciancio, "On bounded distance decoding for general lattices," in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (Lecture Notes in Computer Science), vol. 4110, J. Díaz, K. Jansen, J. D. P. Rolim, and U. Zwick, Eds. New York, NY, USA: Springer-Verlag, 2006, pp. 450-461. (Pubitemid 44577552)
21. J. Loftus, A. May, N. P. Smart, and F. Vercauteren, "On cca-secure somewhat homomorphic encryption" in Proc. Sel. Areas Cryptography, 2011, pp. 55-72.
22. V. Lyubashevsky and D. Micciancio, "On bounded distance decoding, unique shortest vectors, and the minimum distance problem," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 5677, S. Halevi, Ed. New York, NY, USA: Springer-Verlag, 2009, pp. 577-594.
23. D. Micciancio, "Generalized compact knapsacks, cyclic lattices, and efficient one-way functions," Comput. Complexity, vol. 16, no. 4, pp. 365-411, 2007.
24. D. Micciancio, "Lattice-based cryptography," in Encyclopedia of Cryptography and Security, 2nd ed., H. C. A. van Tilborg and S. Jajodia, Eds. New York, NY, USA: Springer-Verlag, 2011, pp. 713-715.
25. P. Q. Nguyen, "Cryptanalysis of the Goldreich-Goldwasser-Halevi cryptosystem from Crypto '97," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 1666, M. J. Wiener, Ed. New York, NY, USA: Springer-Verlag, 1999, pp. 288-304.
26. P. Q. Nguyen, "Breaking fully-homomorphic-encryption challenges," in Cryptology and Network Security (Lecture Notes in Computer Science), vol. 7092, D. Lin, G. Tsudik, and X. Wang, Eds. New York, NY, USA: Springer-Verlag, 2011, pp. 13-14.
27. D. Pointcheval and T. Johansson, Advances in Cryptology (Lecture Notes in Computer Science), vol. 7237. New York, NY, USA: Springer-Verlag, 2012.
28. R. Rivest, L. Adleman, and M. Dertouzos, "On data banks and privacy homomorphisms," in Foundations of Secure Computation. San Francisco, CA, USA: Academic, 1978, pp. 169-177.
29. P. Rogaway, Advances in Cryptology (Lecture Notes in Computer Science), vol. 6841. New York, NY, USA: Springer-Verlag, 2011.
30. P. Scholl and N. P. Smart, "Improved key generation for gentry's fully homomorphic encryption scheme," in Proc. 13th Int. Conf. IMA, vol. 7089. 2011, pp. 10-22.
31. N. P. Smart and F. Vercauteren, "Fully homomorphic encryption with relatively small key and ciphertext sizes," in Public Key Cryptography (Lecture Notes in Computer Science), vol. 6056, P. Q. Nguyen and D. Pointcheval, Eds. New York, NY, USA: Springer-Verlag, 2010, pp. 420-443.
32. D. Stehlé and R. Steinfeld, "Faster fully homomorphic encryption," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 6477, M. Abe, Ed. New York, NY, USA: Springer-Verlag, 2010, pp. 377-394.
33. M. van Dijk, C. Gentry, S. Halevi, and V. Vaikuntanathan, "Fully homomorphic encryption over the integers," in Advances in Cryptology (Lecture Notes in Computer Science), vol. 6110, H. Gilbert, Ed. New York, NY, USA: Springer-Verlag, 2010, pp. 24-43.