Cryptography from learning parity with noise

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

Volumn 7147 LNCS, Issue , 2012, Pages 99-114

  Pietrzak, Krzysztof ^a  

^a INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

AUTHENTICATION PROTOCOLS; CRYPTOGRAPHIC PRIMITIVES; CRYPTOGRAPHIC SCHEMES; EXPONENTIAL TIME; LEARNING PARITY WITH NOISE; LIGHT WEIGHT; PROVABLE SECURITY; PROVABLY SECURE; PSEUDORANDOM GENERATORS; PUBLIC KEYS; QUANTUM ALGORITHMS; RANDOM LINEAR CODES; RF-ID TAGS; SPACE REQUIREMENTS; SYMMETRIC KEY ENCRYPTION; ZERO KNOWLEDGE PROOF;

ALGORITHMS; AUTHENTICATION; CODES (SYMBOLS); COMPUTER SCIENCE; HARDNESS; QUANTUM THEORY; RADIO NAVIGATION;

CRYPTOGRAPHY;

EID: 84856034151     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-27660-6_9     Document Type: Conference Paper

References (48)

1. Applebaum, B., Barak, B., Wigderson, A.: Public-key cryptography from different assumptions. In: Schulman, L.J. (ed.) 42nd ACM STOC, pp. 171-180. ACM Press (2010)
2. 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)
3. Arora, S., Ge, R.: New Algorithms for Learning in Presence of Errors. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 403-415. Springer, Heidelberg (2011)
4. Alekhnovich, M.: More on average case vs approximation complexity. In: 44th FOCS, pp. 298-307. IEEE Computer Society Press (2003)
5. Blum, A., Furst, M.L., Kearns, M.J., Lipton, R.J.: Cryptographic Primitives Based on Hard Learning Problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 278-291. Springer, Heidelberg (1994)
6. Blum, A., Adam Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. J. ACM 50(4), 506-519 (2003)
7. Berlekamp, E.R., McEliece, R.J., van Tilborg, H.C.A.: On the inherent intractability of certain coding problems. IEEE Trans. Information Theory IT-24(3), 384-386 (1978)
8. Banerjee, A., Peikert, C., Rosen, A.: Pseudorandom functions and lattices. Cryptology ePrint Archive, Report 2011/401 (2011), http://eprint.iacr.org/
9. Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993, pp. 62-73. ACM Press (1993)
10. Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai Trees, or How to Delegate a Lattice Basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523-552. Springer, Heidelberg (2010)
11. Cash, D., Kiltz, E., Shoup, V.: The Twin Diffie-Hellman Problem and Applications. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 127-145. Springer, Heidelberg (2008)
12. Coppersmith, D.: Rapid multiplication of rectangular matrices. SIAM J. Comput. 11(3), 467-471 (1982)
13. Dodis, Y., Kiltz, E., Pietrzak, K., Wichs, D.: Message authentication, revisited (manuscript, 2011)
14. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory 31, 469-472 (1985)
15. Feldman, V., Gopalan, P., Khot, S., Ponnuswami, A.K.: New results for learning noisy parities and halfspaces. In: 47th FOCS, pp. 563-574. IEEE Computer Society Press (2006)
16. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) 41st ACM STOC, pp. 169-178. ACM Press (2009)
17. Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. Journal of the ACM 33, 792-807 (1986)
18. Goldwasser, S., Kalai, Y.T., Peikert, C., Vaikuntanathan, V.: Robustness of the learning with errors assumption. In: ICS, pp. 230-240 (2010)
19. Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM Journal on Computing 18(1), 186-208 (1989)
20. Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. Journal of the ACM 38(3), 691-729 (1991)
21. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Ladner, R.E., Dwork, C. (eds.) 40th ACM STOC, pp. 197-206. ACM Press (2008)
22. Gilbert, H., Robshaw, M., Sibert, H.: An active attack against hb+ - a provably secure lightweight authentication protocol. Cryptology ePrint Archive, Report 2005/237 (2005), http://eprint.iacr.org/
23. +. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 361-378. Springer, Heidelberg (2008)
24. Gilbert, H., Robshaw, M.J.B., Seurin, Y.: How to Encrypt with the LPN Problem. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 679-690. Springer, Heidelberg (2008)
25. Hopper, N.J., Blum, M.: Secure Human Identification Protocols. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 52-66. Springer, Heidelberg (2001)
26. Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM Journal on Computing 28(4), 1364-1396 (1999)
27. Heyse, S., Kiltz, E., Lyubashevsky, V., Paar, C., Pietrzak, K.: An efficient authentication protocol based on ring-lpn (manuscript, 2011)
28. Jain, A., Pietrzak, K., Tentes, A.: Commitments and efficient zero-knowledge from hard learning problems (manuscript, 2011)
29. Juels, A., Weis, S.A.: Authenticating Pervasive Devices with Human Protocols. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 293-308. Springer, Heidelberg (2005)
30. Kiltz, E., Pietrzak, K., Cash, D., Jain, A., Venturi, D.: Efficient Authentication from Hard Learning Problems. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 7-26. Springer, Heidelberg (2011)
31. Katz, J., Shin, J.S., Smith, A.: Parallel and concurrent security of the HB and HB+ protocols. Journal of Cryptology 23(3), 402-421 (2010)
32. Levieil, É., Fouque, P.-A.: An Improved LPN Algorithm. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 348-359. Springer, Heidelberg (2006)
33. 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)
34. 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)
35. Luby, M., Rackoff, C.: How to construct pseudorandom permutations from pseudorandom functions. SIAM Journal on Computing 17(2) (1988)
36. Lyubashevsky, V.: The Parity Problem in the Presence of Noise, Decoding Random Linear Codes, and the Subset Sum Problem. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds.) APPROX 2005 and RANDOM 2005. LNCS, vol. 3624, pp. 378-389. Springer, Heidelberg (2005)
37. McEliece, R.J.: A Public-Key Cryptosystem Based On Algebraic Coding Theory. Deep Space Network Progress Report 44, 114-116 (1978)
38. 0.054n). In: ASIACRYPT (2011)
39. Naor, M., Reingold, O.: Synthesizers and their application to the parallel construction of pseudo-random functions. J. Comput. Syst. Sci. 58(2), 336-375 (1999)
40. Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In: Mitzenmacher, M. (ed.) 41st ACM STOC, pp. 333-342. ACM Press (2009)
41. Pietrzak, K.: Subspace LWE (2010) (manuscript)
42. Pointcheval, D., Poupard, G.: A new np-complete problem and public-key identification. Des. Codes Cryptography 28(1), 5-31 (2003)
43. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) 37th ACM STOC, pp. 84-93. ACM Press (2005)
44. Regev, O.: The learning with errors problem (invited survey). In: IEEE Conference on Computational Complexity, pp. 191-204 (2010)
45. Schnorr, C.-P.: Efficient Identification and Signatures for Smart Cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239-252. Springer, Heidelberg (1990)
46. Shamir, A.: An Efficient Identification Scheme based on Permuted Kernels (Extended Abstract). In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 606-609. Springer, Heidelberg (1990)
47. Stern, J.: A Method for Finding Codewords of Small Weight. In: Cohen, G., Godlewski, P. (eds.) Coding Theory 1986. LNCS, vol. 311, pp. 106-113. Springer, Heidelberg (1988)
48. Stern, J.: A New Identification Scheme Based on Syndrome Decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 13-21. Springer, Heidelberg (1994)