Fully homomorphic encryption over the integers with shorter public keys

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6841 LNCS, Issue , 2011, Pages 487-504

  Coron, Jean Sébastien ^a   Mandal, Avradip ^a   Naccache, David ^b   Tibouchi, Mehdi ^a,b  

^a UNIVERSITY OF LUXEMBOURG   (Luxembourg)

^b ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

NUMBER THEORY;

APPROXIMATE GCD; ARITHMETIC OPERATIONS; CONCEPTUAL SIMPLICITY; FULLY HOMOMORPHIC ENCRYPTION; FULLY HOMOMORPHIC ENCRYPTION SCHEMES; HOMOMORPHIC SCHEME; PRACTICAL SYSTEMS; QUADRATIC FORM;

CRYPTOGRAPHY;

EID: 80051993169     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-22792-9_28     Document Type: Conference Paper

References (19)

1. Bach, E.: How to generate factored random numbers. SIAM J. Comput. 17, 179-193 (1988)
2. Boyar, J., Peralta, R., Pochuev, D.: On the multiplicative complexity of boolean functions over the basis (∧,⊕, 1). Theor. Comput. Sci. 235(1), 43-57 (2000)
3. Coron, J.S., Mandal, A., Naccache, D., Tibouchi, M.: Fully Homomorphic Encryption over the Integers with Shorter Public Keys, http://eprint.iacr.org
4. 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)
5. Gentry, C.: A fully homomorphic encryption scheme. Ph.D. thesis, Stanford University (2009), http://crypto.stanford.edu/craig
6. 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)
7. Goldreich, O., Goldwasser, S., Halevi, S.: Public-key cryptosystems from lattice reduction problems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 112-131. Springer, Heidelberg (1997)
8. Grandlung, T., et al.: The GNU Multiple Precision arithmetic library, Version 4.3.2 (2010), http://gmplib.org
9. Lidl, R., Niederreiter, H.: Finite Fields. In: Encyclopedia of Mathematics and its Applications, vol. 20, Addison-Wesley, Reading (1983)
10. Nguyên, P.Q., Stern, J.: The Two Faces of Lattices in Cryptology. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 146-180. Springer, Heidelberg (2001)
11. Nguyen, P.Q.: Personal Communication
12. Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223-238. Springer, Heidelberg (1999)
13. Stein, W.A., et al.: Sage Mathematics Software (Version 4.5.3), The Sage Development Team (2010), http://www.sagemath.org
14. Micciancio, D.: Improving Lattice Based Cryptosystems Using the Hermite Normal Form. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 126-145. Springer, Heidelberg (2001)
15. Pujol, X., Stehlé, D., et al.: Fplll lattice reduction library, http://perso.ens-lyon.fr/xavier.pujol/fplll/
16. 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)
17. Stehlé, D., Steinfeld, R.: Faster Fully Homomorphic Encryption. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 377-394. Springer, Heidelberg (2010)
18. Stehlé, D., Zimmermann, P.: A binary recursive gcd algorithm. In: Buell, D.A. (ed.) ANTS 2004. LNCS, vol. 3076, pp. 411-425. Springer, Heidelberg (2004)
19. Wegman, M.N., Carter, J.L.: New hash functions and their use in authentication and set equality. Journal of Computer and System Sciences 22(3), 265-279 (1981)