Fully homomorphic SIMD operations

Designs, Codes, and Cryptography

Volumn 71, Issue 1, 2014, Pages 57-81

  Smart, N P ^a   Vercauteren, F ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Fully homomorphic encryption; Implementation; SIMD operations

Indexed keywords

EID: 84894656653     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10623-012-9720-4     Document Type: Article

References (25)

1. Boneh D., Di Crescenzo G., Ostrovsky R., Persiano G.: Public key encryption with keyword search. Advances in Cryptology, Eurocrypt 2004(Lecture Notes in Computer Science 3027), 506-522 (2004)
2. Brakerski Z., Gentry C., Vaikuntanathan V.: Fully homomorphic encryption without bootstrapping. Innovations in Theoretical Computer Science, ITCS 2012, 309-325, ACM (2012)
3. Brakerski Z., Vaikuntanathan V.: Fully homomorphic encryption from Ring-LWE and security for key dependent messages. Advances in Cryptology, Crypto 2011. Lecture Notes in Computer Science 6841 6841, 505-524 (2011)
4. Canright D.: A very compact S-Box for AES. Cryptographic Hardware and Embedded Systems, CHES 2005(Lecture Notes in Computer Science 3659), 441-455 (2005)
5. Chor B., Kushilevitz E., Goldreich O., Sudan M.: Private information retrieval. J. ACM. 45, 965-981 (1998)
6. van Dijk M., Gentry C., Halevi S., Vaikuntanathan V.: Fully homomorphic encryption over the integers. Advances in Cryptology, Eurocrypt 2010. Lecture Notes in Computer Science 6110, 24-43 (2010)
7. Cooley J.W., Tukey J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19, 297-301 (1965)
8. Damgård I., Keller M.: Secure multiparty AES. Financial Cryptography, FC 2010(Lecture Notes in Computer Science 6052), 367-374 (2010)
9. Damgård I., Pastro V., Smart N.P., Zakarias S.: Multiparty computation from somewhat homomorphic encryption. Adv. Cryptol. Crypto (2012, in press).
10. Gentry C.: Fully homomorphic encryption using ideal lattices. Symposium on Theory of Computing, STOC 2009, ACM, 169-178, (2009).
11. Gentry C.: A fully homomorphic encryption scheme. Manuscript (2009).
12. Gentry C., Halevi S.: Implementing Gentry's fully-homomorphic encryption scheme. Advances in Cryptology, Eurocrypt 2011. Lecture Notes in Computer Science 6632, 129-148 (2011)
13. Gentry C., Halevi S., Smart N.P.: Fully homomorphic encryption with polylog overhead. Advances in Cryptology, Eurocrypt 2012. Lecture Notes in Computer Science 7237, 465-482 (2012)
14. Gentry C., Halevi S., Smart N.P.: Better bootstrapping in fully homomorphic encryption. Public Key Cryptography, PKC 2012. Lecture Notes in Computer Science 7293, 1-16 (2012)
15. Gentry C., Halevi S., Smart N.P.: Homomorphic evaluation of the AES circuit. Adv. Cryptol. Crypto (2012, in press).
16. Gentry C., Halevi S., Smart N.P.: Ring switching in BGV-style homomorphic encryption. IACR ePrint 2012/240, http://eprint.iacr.org/2012/240/.
17. Good I.J.: The interaction algorithm and practical Fourier analysis. J. R. Stat. Soc. 20, 361-372 (1958)
18. Kushilevitz E., Ostrovsky R.: Replication is not needed: single database, computationally-private information retrieval. Foundations of Computer Science, FoCS '97, pp. 364-373 (1997).
19. Lauter K., Naehrig M., Vaikuntanathan V.: Can homomorphic encryption be practical? Cloud Computing Security Workshop, CCSW 2011, pp. 113-124, ACM, (2011).
20. Pinkas B., Schneider T., Smart N.P., Williams S.C.: Secure two-party computation is practical. Advances in Cryptology, Asiacrypt 2009. Lecture Notes in Computer Science 5912(250-267), 5912-250267 (2009)
21. Rader C.M.: Discrete Fourier transforms when the number of data samples is prime. Proc. IEEE. 56, 1107-1108 (1968)
22. Scholl P., Smart N.P.: Improved key generation for Gentry's fully homomorphic encryption scheme. Cryptography and Coding, IMACC 2011. Lecture Notes in Computer Science 7089, 10-22 (2011).
23. Smart N.P., Vercauteren F.: Fully homomorphic encryption with relatively small key and ciphertext sizes. Public Key Cryptography, PKC 2010. Lecture Notes in Computer Science 6056, 420-443 (2010)
24. Suzuki K., Tonien D., Kurosawa K., Toyota K.: Birthday paradox for multi-collisions. Information Security and Cryptology, ICISC 2006. Lecture Notes in Computer Science 4296, 29-40 (2006)
25. Thomas L.H.: Using a computer to solve problems in physics. Application of Digital Computers, Ginn, Boston (1963).