# Key-Policy Attribute-Based Encryption for Boolean Circuits from Bilinear Maps

Conference paper

First Online:

## Abstract

We propose a Key-policy Attribute-based Encryption (KP-ABE) scheme for (monotone) Boolean circuits based on bilinear maps. The construction is based on secret sharing and just one bilinear map, and it is a proper extension of the KP-ABE scheme in [7] in the sense that it is practically efficient for a class of Boolean circuits which strictly includes all Boolean formulas. Selective security of the proposed scheme in the standard model is proved, and comparisons with the scheme in [5] based on leveled multilinear maps, are provided. Thus, for Boolean circuits representing multilevel access structures, our KP-ABE scheme is more efficient than the one in [5].

## References

- 1.Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: Proceedings of the 2012 ACM Conference on Computer and Communications Security. CCS 2012, pp. 784–796. ACM, New York (2012)Google Scholar
- 2.Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: IEEE Symposium on Security and Privacy, S&P 2007, pp. 321–334. IEEE Computer Society (2007)Google Scholar
- 3.Coron, J.-S., Lepoint, T., Tibouchi, M.: Practical multilinear maps over the integers. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 476–493. Springer, Heidelberg (2013) CrossRefGoogle Scholar
- 4.Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1–17. Springer, Heidelberg (2013) CrossRefGoogle Scholar
- 5.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) CrossRefGoogle Scholar
- 6.Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) STOC, pp. 545–554. ACM (2013), preprint on IACR ePrint 2013/337Google Scholar
- 7.Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encypted data. In: ACM Conference on Computer and Communications Security, pp. 89–98. ACM (2006), preprint on IACR ePrint 2006/309Google Scholar
- 8.Karnin, E.D., Greene, J.W., Hellman, M.E.: On secret sharing systems. IEEE Trans. Inf. Theor.
**29**(1), 35–41 (1983)MathSciNetCrossRefGoogle Scholar - 9.Ostrovsky, R., Sahai, A., Waters, B.: Attribute-based encryption with non-monotonic access structures. In: ACM Conference on Computer and Communications Security, pp. 195–203. ACM (2007), preprint on IACR ePrint 2007/323Google Scholar
- 10.Simmons, G.J.: How to (really) share a secret. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 390–448. Springer, Heidelberg (1990) Google Scholar
- 11.Stinson, D.: Cryptography: Theory and Practice, 3rd edn. Chapman and Hall/CRC, Boca Raton (2005) Google Scholar
- 12.Tassa, T.: Hierarchical threshold secret sharing. J. Cryptology
**20**(2), 237–264 (2007)MathSciNetCrossRefGoogle Scholar - 13.Tassa, T., Dyn, N.: Multipartite secret sharing by bivariate interpolation. J. Cryptology
**22**(2), 227–258 (2008)MathSciNetCrossRefGoogle Scholar

## Copyright information

© Springer International Publishing Switzerland 2015