Advertisement

Compact Adaptively Secure ABE for \(\mathsf {NC^1}\) from k-Lin

  • Lucas KowalczykEmail author
  • Hoeteck Wee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11476)

Abstract

We present compact attribute-based encryption (ABE) schemes for \(\mathsf {NC^1}\) that are adaptively secure under the k-Lin assumption with polynomial security loss. Our KP-ABE scheme achieves ciphertext size that is linear in the attribute length and independent of the policy size even in the many-use setting, and we achieve an analogous efficiency guarantee for CP-ABE. This resolves the central open problem posed by Lewko and Waters (CRYPTO 2011). Previous adaptively secure constructions either impose an attribute “one-use restriction” (or the ciphertext size grows with the policy size), or require q-type assumptions.

Notes

Acknowledgments

We thank Allison Bishop, Sanjam Garg, Rocco Servedio, and Daniel Wichs for helpful discussions.

References

  1. 1.
    Agrawal, S., Chase, M.: Simplifying design and analysis of complex predicate encryption schemes. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part I. LNCS, vol. 10210, pp. 627–656. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-56620-7_22CrossRefGoogle Scholar
  2. 2.
    Attrapadung, N.: Dual system encryption via doubly selective security: framework, fully secure functional encryption for regular languages, and more. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 557–577. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-55220-5_31CrossRefGoogle Scholar
  3. 3.
    Attrapadung, N.: Dual system encryption framework in prime-order groups via computational pair encodings. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016, Part II. LNCS, vol. 10032, pp. 591–623. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53890-6_20CrossRefzbMATHGoogle Scholar
  4. 4.
    Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: IEEE Symposium on Security and Privacy, pp. 321–334. IEEE Computer Society Press, May 2007Google Scholar
  5. 5.
    Blazy, O., Kiltz, E., Pan, J.: (Hierarchical) identity-based encryption from affine message authentication. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 408–425. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44371-2_23CrossRefGoogle Scholar
  6. 6.
    Chen, J., Gay, R., Wee, H.: Improved dual system ABE in prime-order groups via predicate encodings. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 595–624. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46803-6_20CrossRefGoogle Scholar
  7. 7.
    Chen, J., Gong, J., Kowalczyk, L., Wee, H.: Unbounded ABE via bilinear entropy expansion, revisited. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part I. LNCS, vol. 10820, pp. 503–534. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78381-9_19CrossRefGoogle Scholar
  8. 8.
    Chen, J., Wee, H.: Fully, (almost) tightly secure IBE and dual system groups. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 435–460. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40084-1_25CrossRefGoogle Scholar
  9. 9.
    Chen, J., Wee, H.: Semi-adaptive attribute-based encryption and improved delegation for Boolean formula. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 277–297. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-10879-7_16CrossRefGoogle Scholar
  10. 10.
    Cheon, J.H.: Security analysis of the strong Diffie-Hellman problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 1–11. Springer, Heidelberg (2006).  https://doi.org/10.1007/11761679_1CrossRefGoogle Scholar
  11. 11.
    Escala, A., Herold, G., Kiltz, E., Ràfols, C., Villar, J.: An algebraic framework for Diffie-Hellman assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 129–147. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40084-1_8CrossRefGoogle Scholar
  12. 12.
    Fuchsbauer, G., Jafargholi, Z., Pietrzak, K.: A Quasipolynomial Reduction for Generalized Selective Decryption on Trees. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 601–620. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-47989-6_29CrossRefGoogle Scholar
  13. 13.
    Fuchsbauer, G., Konstantinov, M., Pietrzak, K., Rao, V.: Adaptive security of constrained PRFs. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part II. LNCS, vol. 8874, pp. 82–101. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-45608-8_5CrossRefGoogle Scholar
  14. 14.
    Garg, S., Gentry, C., Halevi, S., Sahai, A., Waters, B.: Attribute-based encryption for circuits from multilinear maps. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 479–499. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40084-1_27CrossRefGoogle Scholar
  15. 15.
    Gong, J., Dong, X., Chen, J., Cao, Z.: Efficient IBE with tight reduction to standard assumption in the multi-challenge setting. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016, Part II. LNCS, vol. 10032, pp. 624–654. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53890-6_21CrossRefGoogle Scholar
  16. 16.
    Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, pp. 545–554. ACM Press, New York (2013)Google Scholar
  17. 17.
    Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: Juels, A., Wright, R.N., Vimercati, S. (eds.) ACM CCS 2006, pp. 89–98. ACM Press, New York (2006). Available as Cryptology ePrint Archive Report 2006/309Google Scholar
  18. 18.
    Hemenway, B., Jafargholi, Z., Ostrovsky, R., Scafuro, A., Wichs, D.: Adaptively secure garbled circuits from one-way functions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016, Part III. LNCS, vol. 9816, pp. 149–178. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53015-3_6CrossRefGoogle Scholar
  19. 19.
    Ishai, Y., Kushilevitz, E.: Perfect constant-round secure computation via perfect randomizing polynomials. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 244–256. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-45465-9_22CrossRefGoogle Scholar
  20. 20.
    Jafargholi, Z., Kamath, C., Klein, K., Komargodski, I., Pietrzak, K., Wichs, D.: Be Adaptive, Avoid Overcommitting. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part I. LNCS, vol. 10401, pp. 133–163. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_5CrossRefGoogle Scholar
  21. 21.
    Jafargholi, Z., Wichs, D.: Adaptive security of Yao’s garbled circuits. In: Hirt, M., Smith, A. (eds.) TCC 2016, Part I. LNCS, vol. 9985, pp. 433–458. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53641-4_17CrossRefzbMATHGoogle Scholar
  22. 22.
    Kowalczyk, L., Wee, H.: Compact adaptively secure ABE for NC1 from k-Lin. IACR Cryptology ePrint Archive, 2019:224 (2019)Google Scholar
  23. 23.
    Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: attribute-based encryption and (hierarchical) inner product encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 62–91. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13190-5_4CrossRefGoogle Scholar
  24. 24.
    Lewko, A.B., Sahai, A., Waters, B.: Revocation systems with very small private keys. In: IEEE Symposium on Security and Privacy, pp. 273–285. IEEE Computer Society Press, May 2010Google Scholar
  25. 25.
    Lewko, A., Waters, B.: New techniques for dual system encryption and fully secure HIBE with short ciphertexts. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 455–479. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-11799-2_27CrossRefGoogle Scholar
  26. 26.
    Lewko, A., Waters, B.: New proof methods for attribute-based encryption: achieving full security through selective techniques. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 180–198. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32009-5_12CrossRefGoogle Scholar
  27. 27.
    Okamoto, T., Takashima, K.: Fully secure functional encryption with general relations from the decisional linear assumption. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 191–208. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-14623-7_11CrossRefGoogle Scholar
  28. 28.
    Okamoto, T., Takashima, K.: Fully secure unbounded inner-product and attribute-based encryption. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 349–366. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-34961-4_22CrossRefGoogle Scholar
  29. 29.
    Ostrovsky, R., Sahai, A., Waters, B.: Attribute-based encryption with non-monotonic access structures. In: Ning, P., di Vimercati, S.D.C., Syverson, P.F. (eds.) ACM CCS 2007, pp. 195–203. ACM Press, New York (2007)Google Scholar
  30. 30.
    Parno, B., Raykova, M., Vaikuntanathan, V.: How to delegate and verify in public: verifiable computation from attribute-based encryption. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 422–439. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-28914-9_24CrossRefGoogle Scholar
  31. 31.
    Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005).  https://doi.org/10.1007/11426639_27CrossRefGoogle Scholar
  32. 32.
    Vinod, V., Narayanan, A., Srinathan, K., Rangan, C.P., Kim, K.: On the power of computational secret sharing. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 162–176. Springer, Heidelberg (2003).  https://doi.org/10.1007/978-3-540-24582-7_12CrossRefGoogle Scholar
  33. 33.
    Waters, B.: Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619–636. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-03356-8_36CrossRefGoogle Scholar
  34. 34.
    Wee, H.: Dual system encryption via predicate encodings. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 616–637. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54242-8_26CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.Columbia UniversityNew YorkUSA
  2. 2.CNRS, ENS, PSLParisFrance

Personalised recommendations