Abstract
Attribute-based encryption (ABE) enables fine-grained access control of encrypted data. This technique has been carefully scrutinised by the research community for over a decade, and it has wide theoretical interests as well as practical potentials. Thus, any efficiency improvement of it is highly desirable but non-trivial. In this paper, we demonstrate that the computational costs in ABE can be slightly reduced using Blakley secret sharing. The main reason that contributes to this improvement is a unique feature enjoyed by Blakley secret sharing, i.e. it is more efficient to handle (n, n)-threshold secret sharing compared with Shamir secret sharing. Due to the space limitation, we only describe how to improve key-policy attribute-based encryption (KP-ABE), but our method is very general and it can be used to improve some of its variants similarly, e.g. cipher-policy attribute-based encryption (CP-ABE). This work may also inspire further investigations on Blakley secret sharing, both applying this unique feature to other cryptographic primitives and exploring more undiscovered features.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In this paper, we focus our attentions on key-policy attribute-based encryption (KP-ABE) with a tree-access structure [9], in which the ciphertexts are labelled with sets of attributes and the private keys are associated with tree-access structures, but our proposed method can be applied with some of its variants similarly, e.g. ciphertext-policy attribute-based encryption (CP-ABE) [4].
- 2.
When j parties participate in the secret reconstruction phase where \(j > t\), the sub-matrix \(\mathsf {M}_S\) of \(\mathsf {M}\) is not a square matrix. In this case, we can use the equation \(\bar{a}^T = ({\mathsf {M}_S}^T \cdot \mathsf {M}_S)^{-1} \cdot {\mathsf {M}_S}^T \cdot \bar{s}^T\) to compute \(\bar{a}^T\). Similarly, to recover the secret \(s = a_1\), only the first row of \(({\mathsf {M}_S}^T \cdot \mathsf {M}_S)^{-1} \cdot {\mathsf {M}_S}^T\) needs to be computed.
- 3.
A restriction of the Hadamard matrix is that its order has to be the power of 2, and this may cause some inconvenience in practice. To address this issue, we can either add some dummy entities to make the total number of entities as the power of 2, or we can use the Weighing matrix instead that has similar properties.
- 4.
References
Asmuth, C., Bloom, J.: A modular approach to key safeguarding. IEEE Trans. Inf. Theory 29(2), 208–210 (1983)
Beimel, A.: Secure schemes for secret sharing and key distribution. Technion-Israel Institute of Technology, Faculty of Computer Science (1996)
Benaloh, J., Leichter, J.: Generalized secret sharing and monotone functions. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 27–35. Springer, New York (1990). https://doi.org/10.1007/0-387-34799-2_3
Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: 2007 IEEE Symposium on Security and Privacy (SP 2007), pp. 321–334. IEEE (2007)
Blakley, G.R., et al.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, vol. 48 (1979)
Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_13
Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 207–222. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_13
Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 537–554. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1_34
Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: Proceedings of the 13th ACM Conference on Computer and Communications Security, pp. 89–98. ACM (2006)
Kothari, S.C.: Generalized linear threshold scheme. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 231–241. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_19
Li, J., Huang, X., Li, J., Chen, X., Xiang, Y.: Securely outsourcing attribute-based encryption with checkability. IEEE Trans. Parallel Distrib. Syst. 25(8), 2201–2210 (2013)
Li, M., Shucheng, Y., Zheng, Y., Ren, K., Lou, W.: Scalable and secure sharing of personal health records in cloud computing using attribute-based encryption. IEEE Trans. Parallel Distrib. Syst. 24(1), 131–143 (2012)
Mignotte, M.: How to share a secret. In: Beth, T. (ed.) EUROCRYPT 1982. LNCS, vol. 149, pp. 371–375. Springer, Heidelberg (1983). https://doi.org/10.1007/3-540-39466-4_27
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_5
Acknowledgement
This work was partially supported by the National Natural Science Foundation of China (Grant No. 61572303, 61772326, 61822202, 61672010, 61872087) and Guizhou Key Laboratory of Public Big Data (Grant No. 2019BDKFJJ005). We are very grateful to the anonymous reviewers for their valuable comments on the paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Xia, Z., Yang, B., Zhou, Y., Zhang, M., Mu, Y. (2020). Improvement of Attribute-Based Encryption Using Blakley Secret Sharing. In: Liu, J., Cui, H. (eds) Information Security and Privacy. ACISP 2020. Lecture Notes in Computer Science(), vol 12248. Springer, Cham. https://doi.org/10.1007/978-3-030-55304-3_33
Download citation
DOI: https://doi.org/10.1007/978-3-030-55304-3_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-55303-6
Online ISBN: 978-3-030-55304-3
eBook Packages: Computer ScienceComputer Science (R0)