Fully homomorphic encryption over the integers

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

Volumn 6110 LNCS, Issue , 2010, Pages 24-43

  Van Dijk, Marten ^a   Gentry, Craig ^b   Halevi, Shai ^b   Vaikuntanathan, Vinod ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b IBM RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONCEPTUAL SIMPLICITY; ENCRYPTION SCHEMES; FULLY HOMOMORPHIC ENCRYPTION; HOMOMORPHIC SCHEME; INTEGER GCD; MODULAR ARITHMETIC; POLYNOMIAL RINGS;

IMAGE QUALITY;

CRYPTOGRAPHY;

EID: 77954642756     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-13190-5_2     Document Type: Conference Paper

References (22)

1. Alexi, W., Chor, B., Goldreich, O., Schnorr, C.-P.: Rsa and rabin functions: Certain parts are as hard as the whole. SIAM J. Comput. 17(2), 194-209 (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. Cachin, C., Micali, S., Stadler, M.: Computationally private information retrieval with polylogarithmic communication. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 402-414. Springer, Heidelberg (1999)
4. Coppersmith, D.: Small solutions to polynomial equations, and low exponent RSA vulnerabilities. J. Cryptology 10(4), 233-260 (1997)
5. Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University (2009), http://crypto.stanford.edu/craig
6. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC 2009, pp. 169-178. ACM, New York (2009)
7. Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28(2), 270-299 (1984) (Pubitemid 14586283)
8. 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)
9. Howgrave-Graham, N.: Approximate integer common divisors. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 51-66. Springer, Heidelberg (2001)
10. Ishai, Y., Paskin, A.: Evaluating branching programs on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575-594. Springer, Heidelberg (2007)
11. Karp, R.M., Ramachandran, V.: A Survey of Parallel Algorithms for Shared-Memory Machines. Technical Report CSD-88-408, UC Berkeley (1988)
12. Knuth, D.E.: Seminumerical Algorithms, 3rd edn. The Art of Computer Programming, vol. 2. Addison-Wesley, Reading (1997)
13. Lagarias, J.C.: The computational complexity of simultaneous diophantine approximation problems. SIAM J. Comput. 14(1), 196-209 (1985)
14. Lenstra, A.K.: Factoring multivariate polynomials over algebraic number fields. SIAM J. Comput. 16(3), 591-598 (1987)
15. Lindell, Y., Pinkas, B.: A proof of security of yao's protocol for two-party computation. J. Cryptology 22(2) (2009)
16. Nguyen, P.Q., Shparlinski, I.: On the insecurity of a server-aided RSA protocol. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 21-35. Springer, Heidelberg (2001)
17. Nguyen, 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)
18. Nguyen, P.Q., Stern, J.: Adapting density attacks to low-weight knapsacks. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 41-58. Springer, Heidelberg (2005)
19. Regev, O.: New lattice-based cryptographic constructions. JACM 51(6), 899-942 (2004)
20. Rivest, R., Adleman, L., Dertouzos, M.: On data banks and privacy homomorphisms. In: Foundations of Secure Computation, pp. 169-177. Academic Press, London (1978)
21. van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. Cryptology ePrint Archive, Report 2009/616 (2009), http://eprint.iacr.org/2009/616
22. Yao, A.C.: Protocols for secure computations. In: 23rd Annual Symposium on Foundations of Computer Science - FOCS 1982, pp. 160-164. IEEE, Los Alamitos (1982)