A toolkit for ring-LWE cryptography

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

Volumn 7881 LNCS, Issue , 2013, Pages 35-54

  Lyubashevsky, Vadim ^a   Peikert, Chris ^b   Regev, Oded ^c  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYPTOGRAPHIC APPLICATIONS; CRYPTOGRAPHIC SCHEMES; EFFICIENT IMPLEMENTATION; FULLY HOMOMORPHIC ENCRYPTION; MODULAR ALGORITHMS; NEW APPLICATIONS; PUBLIC KEY CRYPTOSYSTEMS; SYMMETRIC ENCRYPTION SCHEMES;

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE;

PUBLIC KEY CRYPTOGRAPHY;

EID: 84883318384     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-38348-9_3     Document Type: Conference Paper

References (38)

1. Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553-572. Springer, Heidelberg (2010)
2. Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. Theory of Computing Systems 48(3), 535-553 (2011);
3. Preliminary version in STACS 2009
4. Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular-secure encryption based on hard learning problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595-618. Springer, Heidelberg (2009)
5. Babai, L.: On Lovász' lattice reduction and the nearest lattice point problem. Combinatorica 6(1), 1-13 (1986);
6. Preliminary version in Mehlhorn, K. (ed.) STACS 1985. LNCS, vol. 182, pp. 13-20. Springer, Heidelberg (1984)
7. Banerjee, A., Peikert, C., Rosen, A.: Pseudorandom functions and lattices. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 719-737. Springer, Heidelberg (2012)
8. Bosma, W.: Canonical bases for cyclotomic fields. Appl. Algebra Eng. Commun. Comput. 1, 125-134 (1990)
9. Boyen, X.: Lattice mixing and vanishing trapdoors: A framework for fully secure short signatures and more. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 499-517. Springer, Heidelberg (2010)
10. Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: ICTS, pp. 309-325 (2012)
11. Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505-524. Springer, Heidelberg (2011)
12. Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. J. Cryptology 25(4), 601-639(2010);
13. Preliminary version in Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523-552. Springer, Heidelberg (2010)
14. Ducas, L., Durmus, A.: Ring-LWE in polynomial rings. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 34-51. Springer, Heidelberg (2012)
15. Erdös, P.: On the coefficients of the cyclotomic polynomial. Bulletin of the American Mathematical Society 52(2), 179-184 (1946)
16. Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University (2009), http://crypto.stanford.edu/craig
17. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169-178 (2009)
18. Gentry, C.: Toward basing fully homomorphic encryption on worst-case hardness. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 116-137. Springer, Heidelberg (2010)
19. Gentry, C., Halevi, S., Peikert, C., Smart, N.P.: Ring switching in BGVstyle homomorphic encryption. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 19-37. Springer, Heidelberg (2012), Full version at http://eprint.iacr.org/2012/240
20. Gentry, C., Halevi, S., Smart, N.P.: Fully homomorphic encryption with polylog overhead. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 465-482. Springer, Heidelberg (2012)
21. Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the AES circuit. In: Safavi-Naini, R. (ed.) CRYPTO 2012. LNCS, vol. 7417, pp. 850-867. Springer, Heidelberg (2012)
22. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC, pp. 197-206 (2008)
23. Güneysu, T., Lyubashevsky, V., Pöppelmann, T.: Practical lattice-based cryptography: A signature scheme for embedded systems. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 530-547. Springer, Heidelberg (2012)
24. Lyubashevsky, V.: Fiat-Shamir with aborts: Applications to lattice and factoring-based signatures. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 598-616. Springer, Heidelberg (2009)
25. Lyubashevsky, V.: Lattice signatures without trapdoors. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 738-755. Springer, Heidelberg (2012)
26. Lyubashevsky, V., Micciancio, D.: Generalized compact knapsacks are collision resistant. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part II. LNCS, vol. 4052, pp. 144-155. Springer, Heidelberg (2006) (Pubitemid 44113243)
27. Lyubashevsky, V., Micciancio, D.: Asymptotically efficient lattice-based digital signatures. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 37-54. Springer, Heidelberg (2008)
28. Lyubashevsky, V., Micciancio, D., Peikert, C., Rosen, A.: SWIFFT: A modest proposal for FFT hashing. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 54-72. Springer, Heidelberg (2008)
29. Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1-23. Springer, Heidelberg (2010)
30. Micciancio, D.: Generalized compact knapsacks, cyclic lattices, and efficient one-way functions. Computational Complexity 16(4), 365-411 (2002);
31. Preliminary version in FOCS 2002
32. Micciancio, D., Peikert, C.: Trapdoors for lattices: Simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700-718. Springer, Heidelberg (2012)
33. Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem. In: STOC, pp. 333-342 (2009)
34. Peikert, C., Rosen, A.: Lattices that admit logarithmic worst-case to average-case connection factors. In: STOC, pp. 478-487 (2007)
35. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6), 1-40 (2005); Preliminary version in STOC
36. Smart, N.P., Vercauteren, F.: Fully homomorphic SIMD operations. Cryptology ePrint Archive, Report 2011/133 (2011), http://eprint.iacr.org/
37. Stehlé, D., Steinfeld, R.: Making NTRU as secure as worst-case problems over ideal lattices. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 27-47. Springer, Heidelberg (2011)
38. Stehlé, D., Steinfeld, R., Tanaka, K., Xagawa, K.: Efficient public key encryption based on ideal lattices. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 617-635. Springer, Heidelberg (2009)