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A Survey on Identity-Based Encryption from Lattices

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Mathematical Modelling for Next-Generation Cryptography

Part of the book series: Mathematics for Industry ((MFI,volume 29))

Abstract

Lattice-based cryptography is one of the most important topics in the area of cryptography, because of its (asymptotic) efficiency, post-quantum security, and expressiveness. In this survey, we provide an overview of lattice-based identity-based encryption (IBE), which is also an important topic in the area. In more details, we first introduce dual Regev public key encryption. Then, we change it to obtain Gentry–Peikert–Vaikuntanathan IBE, which is secure in the random oracle model. We then provide a framework for capturing constructions in the standard model. Then, by instantiating the framework, we show that we can capture the Cash–Hofheinz–Kiltz–Peikert and Agrawal–Boneh–Boyen scheme. Finally, we mention several recent works aiming at reducing parameters or tight security reductions.

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Notes

  1. 1.

    We note that even if this probability is noticeable, the security proof requires additional complication in the simulation and the computation of the advantage [7, 44].

References

  1. S. Agrawal, D. Boneh, X. Boyen, Efficient lattice (H)IBE in the standard model, in EUROCRYPT (2010), pp. 553–572

    Google Scholar 

  2. S. Agrawal, D. Boneh, X. Boyen, Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE, in CRYPTO (2010), pp. 98–115

    Google Scholar 

  3. M. Ajtai, Generating hard instances of the short basis problem, in ICALP (1999), pp. 1–9

    Google Scholar 

  4. J. Alwen, C. Peikert, Generating shorter bases for hard random lattices, in STACS (2009), pp. 75–86

    Google Scholar 

  5. D. Apon, X. Fan, F. Liu, Fully-secure lattice-based IBE as compact as PKE, in IACR Cryptology ePrint Archive 2016:125 (2016)

    Google Scholar 

  6. N. Attrapadung, G. Hanaoka, S. Yamada, A framework for identity-based encryption with almost tight security, in ASIACRYPT (1) (2015), pp. 521–549

    Google Scholar 

  7. M. Bellare, T. Ristenpart, Simulation without the artificial abort: simplified proof and improved concrete security for waters’ IBE scheme, in EUROCRYPT (2009), pp. 407–424

    Google Scholar 

  8. O. Blazy, E. Kiltz, J. Pan, (hierarchical) identity-based encryption from affine message authentication, in CRYPTO (2014), pp. 408–425

    Google Scholar 

  9. D. Boneh, M. Franklin, Identity-based encryption from the weil pairing, in CRYPTO (2001), pp. 213–229

    Google Scholar 

  10. D. Boneh, X. Boyen, Efficient selective-id secure identity-based encryption without random oracles, in EUROCRYPT (2004), pp. 223–238

    Google Scholar 

  11. D. Boneh, X. Boyen, Secure identity based encryption without random oracles, in CRYPTO (2004), pp. 443–459

    Google Scholar 

  12. D. Boneh, X. Boyen, E.J. Goh, Hierarchical identity based encryption with constant size ciphertext, in EUROCRYPT (2005), pp. 440–456

    Google Scholar 

  13. D. Boneh, C. Gentry, S. Gorbunov, S. Halevi, V. Nikolaenko, G. Segev, V. Vaikuntanathan, D. Vinayagamurthy, Fully key-homomorphic encryption, arithmetic circuit ABE and compact garbled circuits, in EUROCRYPT (2014), pp. 533–556

    Google Scholar 

  14. X. Boyen, Lattice mixing and vanishing trapdoors: a framework for fully secure short signatures and more, in PKC (2010), pp. 499–517

    Google Scholar 

  15. X. Boyen, B. Waters, Anonymous hierarchical identity-based encryption (Without Random Oracles), in CRYPTO (2006), pp. 290–307

    Google Scholar 

  16. X. Boyen, Q. Li, Towards tightly secure lattice short signature and ID-based encryption, in ASIACRYPT (to appear) (2016)

    Google Scholar 

  17. Z. Brakerski, V. Vaikuntanathan, Lattice-based FHE as secure as PKE, in ITCS (2014), pp. 1–12

    Google Scholar 

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

    Google Scholar 

  19. R. Canetti, S. Halevi, J. Katz, A forward-secure public-key encryption scheme, in EUROCRYPT (2003), pp. 255–271

    Google Scholar 

  20. D. Cash, D. Hofheinz, E. Kiltz, C. Peikert, Bonsai trees, or how to delegate a lattice basis, in EUROCRYPT (2010), pp. 523–552

    Google Scholar 

  21. J. Chen, H. Wee, Fully, (almost) tightly secure IBE and dual system groups, in CRYPTO (2013), pp. 435–460

    Google Scholar 

  22. C. Cocks, An identity based encryption scheme based on quadratic residues, in IMA International Conference (2001), pp. 360–363

    Google Scholar 

  23. C. Gentry, Practical identity-based encryption without random oracles, in EUROCRYPT (2006), pp. 445–464

    Google Scholar 

  24. C. Gentry, A. Silverberg, Hierarchical ID-based cryptography, in ASIACRYPT (2002), pp. 548–566

    Google Scholar 

  25. C. Gentry, C. Peikert, V. Vaikuntanathan, Trapdoors for hard lattices and new cryptographic constructions, in STOC (2008), pp. 197–206

    Google Scholar 

  26. S. Gorbunov, V. Vaikuntanathan, H. Wee, Attribute-based encryption for circuits, in STOC (2013), pp. 545–554

    Google Scholar 

  27. J. Gong, J. Chen, X. Dong, Z. Cao, S. Tang, Extended nested dual system groups, revisited, in PKC(1) (2016), pp. 133–163

    Google Scholar 

  28. K. Haralambiev, T. Jager, E. Kiltz, V. Shoup, Simple and efficient public-key encryption from computational Diffie-Hellman in the standard model, in PKC (2010), pp. 1–18

    Google Scholar 

  29. S. Heng, K. Kurosawa, \(k\)-Resilient identity-based encryption in the standard model, in CT-RSA (2004), pp. 67–80

    Google Scholar 

  30. D. Hofheinz, E. Kiltz, Programmable hash functions and their applications, in CRYPTO (2008), pp. 21–38

    Google Scholar 

  31. D. Hofheinz, J. Koch, C. Striecks, Identity-based encryption with (almost) tight security in the multi-instance, multi-ciphertext setting, in PKC (2015), pp. 799–822

    Google Scholar 

  32. C. Jutla, A. Roy, Shorter quasi-adaptive NIZK proofs for linear subspaces, in ASIACRYPT (2013), pp. 1–20

    Google Scholar 

  33. S. Katsumata, S. Yamada, Partitioning via non-linear polynomial functions: more compact IBEs from ideal lattices and bilinear maps, in ASIACRYPT (to appear) (2016)

    Google Scholar 

  34. V. Lyubashevsky, C. Peikert, O. Regev, On ideal lattices and learning with errors over rings, in EUROCRYPT (2010), pp. 1–23

    Google Scholar 

  35. V. Lyubashevsky, C. Peikert, O. Regev, A toolkit for ring-LWE cryptography, in EUROCRYPT (2013), pp. 35–54

    Google Scholar 

  36. D. Micciancio, C. Peikert, Trapdoors for lattices: simpler, tighter, faster, smaller, in EUROCRYPT (2012), pp. 700–718

    Google Scholar 

  37. D. Naccache, Secure and practical identity-based encryption. IET Inf. Secur. 1(2), 59–64 (2007)

    Article  Google Scholar 

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

    Google Scholar 

  39. C. Peikert, A decade of lattice cryptography, IACR Cryptology ePrint Archive, Report 2015/939

    Google Scholar 

  40. O. Regev, On lattices, learning with errors, random linear codes, and cryptography, in STOC (2005), pp. 843–873

    Google Scholar 

  41. R. Sakai, K. Ohgishi, M. Kasahara, Cryptosystems based on pairing over elliptic curve, in The 2000 Symposium on Cryptography and Information Security (in Japanese) (2000)

    Google Scholar 

  42. A. Shamir, Identity-based cryptosystems and signature schemes, in CRYPTO (1984), pp. 47–53

    Google Scholar 

  43. K. Singh, C. Pandu Rangan, A.K. Banerjee, Adaptively secure efficient lattice (H)IBE in standard model with short public parameters, in SPACE (2012), pp. 153–172

    Google Scholar 

  44. B. Waters, Efficient identity-based encryption without random oracles, in UROCRYPT (2005), pp. 114–127

    Google Scholar 

  45. B. Waters, Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions, in CRYPTO (2009), pp. 619–636

    Google Scholar 

  46. S. Yamada, Adaptively secure identity-based encryption from lattices with asymptotically shorter public parameters, in EUROCRYPT (2) (2016), pp. 32–62

    Google Scholar 

  47. S. Yamada, Y. Kawai, G. Hanaoka, N. Kunihiro, Public key encryption schemes from the (B)CDH assumption with better efficiency. IEICE Trans. 93–A(11), 1984–1993 (2010)

    Article  Google Scholar 

  48. S. Yamada, G. Hanaoka, N. Kunihiro, Two-dimensional representation of cover free families and its applications: short signatures and more, in CT-RSA (2012), pp. 260–277

    Google Scholar 

  49. T. Yamakawa, S. Yamada, K. Nuida, G. Hanaoka, N. Kunihiro, Reducing public key sizes in bounded CCA-secure KEMs with optimal ciphertext length, ISC 2013 (2015), pp. 100–109 (Short Paper)

    Google Scholar 

  50. J. Zhang, Y. Chen, Z. Zhang, Programmable hash functions from lattices: short signatures and IBEs with small key sizes, in CRYPTO(1), pp. 214–243

    Google Scholar 

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Authors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology (AIST), Tokyo Waterfront Bio-IT Research Building, 2-4-7 Aomi, Koto-ku, Tokyo, 135-0064, Japan

    Goichiro Hanaoka

  2. Tokyo Waterfront Bio-IT Research Building, 2-4-7 Aomi, Koto-ku, Tokyo, 135-0064, Japan

    Shota Yamada

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  1. Goichiro Hanaoka
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  2. Shota Yamada
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Correspondence to Shota Yamada .

Editor information

Editors and Affiliations

  1. Kyushu University, Fukuoka, Japan

    Tsuyoshi Takagi

  2. Kyushu University, Fukuoka, Japan

    Masato Wakayama

  3. Tokyo Institute of Technology, Tokyo, Japan

    Keisuke Tanaka

  4. The University of Tokyo, Kashiwa, Japan

    Noboru Kunihiro

  5. University of the Ryukyus, Nakagami-gun, Japan

    Kazufumi Kimoto

  6. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Dung Hoang Duong

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Hanaoka, G., Yamada, S. (2018). A Survey on Identity-Based Encryption from Lattices. In: Takagi, T., Wakayama, M., Tanaka, K., Kunihiro, N., Kimoto, K., Duong, D. (eds) Mathematical Modelling for Next-Generation Cryptography. Mathematics for Industry, vol 29. Springer, Singapore. https://doi.org/10.1007/978-981-10-5065-7_19

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  • DOI: https://doi.org/10.1007/978-981-10-5065-7_19

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  • Online ISBN: 978-981-10-5065-7

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