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Approximate-Deterministic Public Key Encryption from Hard Learning Problems

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Progress in Cryptology – INDOCRYPT 2016 (INDOCRYPT 2016)

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Abstract

We introduce the notion of approximate-deterministic public key encryption (A-DPKE), which extends the notion of deterministic public key encryption (DPKE) by allowing the encryption algorithm to be “slightly” randomized. However, a ciphertext convergence property is required for A-DPKE such that the ciphertexts of a message are gathering in a small metric space, while ciphertexts of different messages can be distinguished easily. Thus, A-DPKE maintains the convenience of DPKE in fast search and de-duplication on encrypted data, and encompasses new constructions. We present two simple constructions of A-DPKE, respectively from the learning parity with noise and the learning with errors assumptions.

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References

  1. Alekhnovich, M.: More on average case vs approximation complexity. In: FOCS 2003, pp. 298–307. IEEE (2003)

    Google Scholar 

  2. Akavia, A., Bogdanov, A., Guo, S., Kamath, A., Rosen, A.: Candidate weak pseudorandom functions in AC0 \(\circ \) MOD2. In: ITCS 2014, pp. 251–259. ACM (2014)

    Google Scholar 

  3. Alwen, J., Krenn, S., Pietrzak, K., Wichs, D.: Learning with rounding, revisited - new reductions, properties and applications. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 57–74. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40041-4_4

    Chapter  Google Scholar 

  4. Bellare, M., Boldyreva, A., O’Neill, A.: Deterministic and efficiently searchable encryption. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 535–552. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74143-5_30

    Chapter  Google Scholar 

  5. Bellare, M., Fischlin, M., O’Neill, A., Ristenpart, T.: Deterministic encryption: definitional equivalences and constructions without random oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 360–378. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85174-5_20

    Chapter  Google Scholar 

  6. Boldyreva, A., Fehr, S., O’Neill, A.: On notions of security for deterministic encryption, and efficient constructions without random oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 335–359. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85174-5_19

    Chapter  Google Scholar 

  7. Bogdanov, A., Guo, S., Masny, D., Richelson, S., Rosen, A.: On the hardness of learning with rounding over small modulus. ePrint Archive 2015/769 (2015)

    Google Scholar 

  8. Bellare, M., Hoang, V.T.: Resisting randomness subversion: fast deterministic and hedged public-key encryption in the standard model. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 627–656. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46803-6_21

    Google Scholar 

  9. Bellare, M., Hoang, V.T., Keelveedhi, S.: Instantiating random oracles via UCEs. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 398–415. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40084-1_23

    Chapter  Google Scholar 

  10. Bellare, M., Kiltz, E., Peikert, C., Waters, B.: Identity-based (lossy) trapdoor functions and applications. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 228–245. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29011-4_15

    Chapter  Google Scholar 

  11. Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehlé, D.: Classical hardness of learning with errors. In: STOC 2013, pp. 575–584. ACM (2013)

    Google Scholar 

  12. 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). doi:10.1007/978-3-642-29011-4_42

    Chapter  Google Scholar 

  13. Brakerski, Z., Segev, G.: Better security for deterministic public-key encryption: the auxiliary-input setting. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 543–560. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22792-9_31

    Chapter  Google Scholar 

  14. Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002). doi:10.1007/3-540-46035-7_4

    Chapter  Google Scholar 

  15. Döttling, N., Müller-Quade, J.: Lossy codes and a new variant of the learning-with-errors problem. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 18–34. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38348-9_2

    Chapter  Google Scholar 

  16. Döttling, N., Müller-Quade, J., Nascimento, A.C.A.: IND-CCA secure cryptography based on a variant of the LPN problem. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 485–503. Springer, Heidelberg (2012). doi:10.1007/978-3-642-34961-4_30

    Chapter  Google Scholar 

  17. Fuller, B., O’Neill, A., Reyzin, L.: A unified approach to deterministic encryption: new constructions and a connection to computational entropy. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 582–599. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28914-9_33

    Chapter  Google Scholar 

  18. Goldwasser, S., Kalai, Y.T., Peikert, C., Vaikuntanathan, V.: Robustness of the learning with errors assumption. In: ICS 2010, pp. 230–240. Tsinghua University Press (2010)

    Google Scholar 

  19. Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  20. Gentry, C., Peikert, C., Vaikuntanathan, V.: How to use a short basis: trapdoors for hard lattices and new cryptographic constructions. In: STOC 2008, pp. 197–206. ACM (2008)

    Google Scholar 

  21. Damgård, I., Park, S.: How practical is public-key encryption based on LPN? ePrint Archive, 2012/699 (2012)

    Google Scholar 

  22. Heyse, S., Kiltz, E., Lyubashevsky, V., Paar, C., Pietrzak, K.: Lapin: an efficient authentication protocol based on Ring-LPN. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 346–365. Springer, Heidelberg (2012). doi:10.1007/978-3-642-34047-5_20

    Chapter  Google Scholar 

  23. Kiltz, E., Masny, D., Pietrzak, K.: Simple chosen-ciphertext security from low-noise LPN. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 1–18. Springer, Heidelberg (2014). doi:10.1007/978-3-642-54631-0_1

    Chapter  Google Scholar 

  24. Katz, J., Vaikuntanathan, V.: Smooth projective hashing and password-based authenticated key exchange from lattices. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 636–652. Springer, Heidelberg (2009). doi:10.1007/978-3-642-10366-7_37

    Chapter  Google Scholar 

  25. 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). doi:10.1007/978-3-642-13190-5_1

    Chapter  Google Scholar 

  26. Meurer, A.: A coding-theoretic approach to cryptanalysis. Ph.D. dissertation thesis (2012)

    Google Scholar 

  27. Micciancio, D., Mol, P.: Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 465–484. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22792-9_26

    Chapter  Google Scholar 

  28. 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). doi:10.1007/978-3-642-29011-4_41

    Chapter  Google Scholar 

  29. Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In STOC 2009, pp. 333–342. ACM (2009)

    Google Scholar 

  30. Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85174-5_31

    Chapter  Google Scholar 

  31. Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: STOC 2008, pp. 187–196. ACM (2008)

    Google Scholar 

  32. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC 2005, pp. 84–93. ACM (2005)

    Google Scholar 

  33. Raghunathan, A., Segev, G., Vadhan, S.: Deterministic public-key encryption for adaptively chosen plaintext distributions. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 93–110. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38348-9_6

    Chapter  Google Scholar 

  34. Sun, X., Li, B., Lu, X.: Cramer-shoup like chosen ciphertext security from LPN. In: Lopez, J., Wu, Y. (eds.) ISPEC 2015. LNCS, vol. 9065, pp. 79–95. Springer, Heidelberg (2015). doi:10.1007/978-3-319-17533-1_6

    Chapter  Google Scholar 

  35. Wee, H.: Dual projective hashing and its applications — lossy trapdoor functions and more. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 246–262. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29011-4_16

    Chapter  Google Scholar 

  36. Wichs, D.: Barriers in cryptography with weak, correlated and leaky sources. In: ITCS 2013, pp. 111–126. ACM (2013)

    Google Scholar 

  37. Xie, X., Xue, R., Zhang, R.: Deterministic public key encryption and identity-based encryption from lattices in the auxiliary-input setting. In: Visconti, I., Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 1–18. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32928-9_1

    Chapter  Google Scholar 

  38. Yu, Y., Zhang, J.: Cryptography with auxiliary input and trapdoor from constant-noise LPN. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 214–243. Springer, Heidelberg (2016). doi:10.1007/978-3-662-53018-4_9. ePrint Archive, 2016/514

    Chapter  Google Scholar 

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Acknowledgments

We are grateful to anonymous reviewers for their inspiring comments. Besides, we thank Yuanyuan Gao and Jingnan He for helpful discussions. Yamin Liu is supported by the National Natural Science Foundation of China (No. 61502480). Xianhui Lu is supported the by National Natural Science Foundation of China (No. 61572495, No. 61272534). Bao Li and Fuyang Fang are supported by the National Natural Science Foundation of China (No. 61379137) and the National Basic Research Program of China (973 project) (No. 2013CB338002).

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Authors and Affiliations

  1. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, China

    Yamin Liu, Xianhui Lu, Bao Li, Wenpan Jing & Fuyang Fang

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Yamin Liu, Xianhui Lu, Bao Li, Wenpan Jing & Fuyang Fang

  3. University of Chinese Academy of Sciences, Beijing, China

    Xianhui Lu, Bao Li & Fuyang Fang

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  1. Yamin Liu
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Correspondence to Xianhui Lu .

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Editors and Affiliations

  1. University of Haifa , Haifa, Israel

    Orr Dunkelman

  2. Indraprashtha Institute of Information Technology (IIIT-D), New Delhi, India

    Somitra Kumar Sanadhya

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Liu, Y., Lu, X., Li, B., Jing, W., Fang, F. (2016). Approximate-Deterministic Public Key Encryption from Hard Learning Problems. In: Dunkelman, O., Sanadhya, S. (eds) Progress in Cryptology – INDOCRYPT 2016. INDOCRYPT 2016. Lecture Notes in Computer Science(), vol 10095. Springer, Cham. https://doi.org/10.1007/978-3-319-49890-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-49890-4_2

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