Accelerating NTRU based homomorphic encryption using GPUs

2014 IEEE High Performance Extreme Computing Conference, HPEC 2014

Volumn , Issue , 2014, Pages

  Dai, Wei ^a   Doroz, Yarkin ^a   Sunar, Berk ^a  

^a Worcester Polytechnic Institute   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; DISCRETE FOURIER TRANSFORMS; POLYNOMIALS; PROGRAM PROCESSORS;

CHINESE REMAINDER THEOREM; FULLY HOMOMORPHIC ENCRYPTION SCHEMES; HO-MOMORPHIC ENCRYPTIONS; MODULAR MULTIPLICATION; POLYNOMIAL ARITHMETIC; RELINEARIZATION; SOFTWARE IMPLEMENTATION; SOMEWHAT HOMOMORPHIC ENCRYPTIONS;

CRYPTOGRAPHY;

EID: 84946686695     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/HPEC.2014.7041001     Document Type: Conference Paper

References (35)

1. c. Gentry, "A fully homomorphic encryption scheme," Ph. D. dissertation, Stanford University, 2009.
2. A. Lopez-Alt, E. Tromer, and V. Vaikuntanathan, "On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption," in STOC, 2012.
3. M. van Dijk, C. Gentry, S. Halevi, and V. Vaikuntanathan, "Fully homomorphic encryption over the integers," in EUROCRYPT, 2010, pp. 24-43.
4. J.-S. Coron, A. Mandai, D. Naccache, and M. Tibouchi, "Fully homomorphic encryption over the integers with shorter public keys," in CRYPTO, 2011, pp. 487-504.
5. J.-S. Coron, D. Naccache, and M. Tibouchi, "Public key compression and modulus switching for fully homomorphic encryption over the integers," in EUROCRYPT, 2012, pp. 446-464.
6. Z. Brakerski and V. Vaikuntanathan, "Efficient fully homomorphic encryption from (standard) LWE," in FOCS, 2011, pp. 97-106.
7. C. Gentry, S. Halevi, and N. P. Smart, "Better bootstrapping in fully homomorphic encryption," IACR Cryptology ePrint Archive 2011/680, vol. 2011, 2011.
8. "Fully homomorphic encryption with polylog overhead;' IACR Cryptology ePrint Archive Report 2011/566, 2011, http://eprint. iacr. org/.
9. "Homomorphic evaluation of the AES circuit," lACR Cryptology ePrint Archive, vol. 2012,2012.
10. Y. Doroz, Y. Hu, and B. Sunar, "Homomorphic AES evaluation using NTRU. " Cryptology ePrint Archive, Report 2014/039. 2014, http://eprinLiacr. orgi.
11. C. Gentry and S. Halevi, "Implementing Gentry's fully-homomorphic encryption scheme," in EUROCRYPT, 2011, pp. 129-148.
12. Z. Brakerski, C. Gentry, and V. Vaikuntanathan, "Fully homomorphic encryption without bootstrapping," Electronic Colloquium on Computational Complexity (ECCC), vol. 18, p. 111,2011.
13. N. P. Smart and F. Vercauteren," Fully homomorphic SIMD operations," IACR Cryptology ePrint Archive, vol. 2011, p. 133, 2011.
14. Z. Brakerski, C. Gentry, and S. Halevi, "Packed ciphertexts in LWEbased homomorphic encryption," 1ACR Cryptology ePrint Archive, vol. 2012, p. 565, 2012.
15. J.-S. Coron, T. Lepoint, and M. Tibouchi, "Batch fully homomorphic encryption over the integers," IACR Cryptology ePrint Archive, vol. 2013, p. 36, 2013.
16. w. Wang, Y. Hu, L. Chen, X. Huang, and B. Sunar, "Accelerating fully homomorphic encryption using GPU," in HPEC, 2012, pp. 1-5.
17. D. Cousins, K. Rohloff, R. Schantz, and C. Peikert, "SIPHER: Scalable implementation of primitives for homomorphic encrytion," Internet Source, September 20 II.
18. D. Cousins, K. Rohloff, C. Peikert, and R. E. Schantz, "An update on SIPHER (scalable implementation of primitives for homomorphic encRyption)-FPGA implementation using simulink," in HPEC, 2012, pp. 1-5.
19. c. Moore, N. Hanley, J. McAllister, M. O'Neill, E. O'Sullivan, and X. Cao, "Targeting FPGA DSP slices for a large integer multiplier for integer based FHE," Workshop on Applied Homomorphic Cryptography, vol. 7862,2013.
20. X. Cao, C. Moore, M. O'Neill, N. Hanley, and E. O'Sullivan, "Accelerating fully homomorphic encryption over the integers with super-size hardware multiplier and modular reduction," Under Review, 2013.
21. W. Wang and X. Huang, "FPGA implementation of a large-number multiplier for fully homomorphic encryption," in 1SCAS, 2013, pp. 2589-2592.
22. Y. Doroz, E. Oztiirk, and B. Sunar, "Evaluating the hardware performance of a million-bit multiplier," in Digital System Design (DSD), 2013 16th Euromicro Conference on, 2013.
23. "Accelerating fully homomorphic encryption in hardware," 2013, draft, Under Review. [Online]. Available: http://ecewp. ece. wpi. edu/wordpress/vernam/filesl20 13/091 Accelerating-Full y-Homomorphic-Encryption-in-Hardware. pdf
24. c. Gentry and S. Halevi, "Fully homomorphic encryption without squashing using depth-3 arithmetic circuits," lACR Cryptology ePrint Archive, vol. 2011, p. 279, 2011.
25. N. P. Smart and F. Vercauteren, "Fully homomorphic encryption with relatively small key and ciphertext sizes," in Public Key Cryptography, 2010, pp. 420-443.
26. w. Wang, Y. Hu, L. Chen, X. Huang, and B. Sunar, "Exploring the feasibility of fully homomorphic encryption," IEEE Transactions on Computers, vol. 99, no. PrePrints, p. 1, 2013.
27. D. Stehle and R. Steinfeld, "Making ntru as secure as worst-case problems over ideal lattices," Advances in Cryptology-EUROCRYPT, 11, pp. 27-4, 20 II.
28. D. D. A. Schiinhage and V. Strassen, "Schnelle multiplikation grosser zahlen," Computing, vol. 7, no. 3-4, pp. 281-292, 1971.
29. N. Emmart and C. C. Weems, "High precision integer multiplication with a gpu using strassen's algorithm with multiple fft sizes," Parallel Processing Letters, vol. 21, no. 03, pp. 359-375, 2011.
30. J. W. Cooley and 1. W. Tukey, "An algorithm for the machine calculation of complex fourier series," Math. comput, vol. 19, no. 90, pp. 297-301, 1965.
31. D. H. Bailey, "Ffts in external of hierarchical memory," in Proceedings of the 1989 ACM/IEEE conference on Supercomputing. ACM, 1989, pp. 234-242.
32. Y. Doriiz, A. Shahverdi, T. Eisenbarth, and B. Sunar, "Toward practical homomorphic evaluation of block ciphers using prince," Cryptology ePrint Archive, Report 2014/233, 2014, http://eprint. iacr. org/.
33. J. Borghoff and et al., "PRINCE, a low-latency block cipher for pervasive computing applications," in ASIA CRYPT 2012, ser. LNCS, X. Wang and K. Sako, Eds. Springer Berlin Heidelberg, 2012, vol. 7658.
34. D. Canright, "A very compact S-Box for AES," in Cryptographic Hardware and Embedded Systems CHES 2005, ser. Lecture Notes in Computer Science, 1. R. Rao and B. Sunar, Eds. Springer Berlin Heidelberg, 2005, vol. 3659, pp. 441-455.
35. V. Shoup, NTL: A Library for doing Number Theory. [Online]. Available: http://www. shoup. netlntl/