Abstract
To enhance the user’s privacy in electronic ID, anonymous credential systems have been researched. In the anonymous credential system, a trusted issuing organization first issues a certificate certifying the user’s attributes to a user. Then, in addition to the possession of the certificate, the user can anonymously prove only the necessary attributes. Previously, an anonymous credential system was proposed, where CNF (Conjunctive Normal Form) formulas on attributes can be proved. The advantage is that the attribute proof in the authentication has the constant size for the number of attributes that the user owns and the size of the proved formula. Thus, various expressive logical relations on attributes can be efficiently verified. However, the previous system has a limitation: the proved CNF formulas cannot include any negation. Therefore, in this paper, we propose an anonymous credential system with constant-size attribute proofs such that the user can prove CNF formulas with negations. For the proposed system, we extend the previous accumulator for the limited CNF formulas to verify CNF formulas with negations.
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
References
Abe, M., Fuchsbauer, G., Groth, J., Haralambiev, K., Ohkubo, M.: Structure-preserving signatures and commitments to group elements. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 209–236. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_12
Abe, M., Haralambiev, K., Ohkubo, M.: Singing on elements in bilinear groups for modular protocol design. Cryptology ePrint Archive, Report 2010/133 (2010). http://eprint.iacr.org/. (This was merged and presented in [1])
Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_3
Begum, N., Nakanishi, T., Funabiki, N.: Efficient proofs for CNF formulas on attributes in pairing-based anonymous credential system. In: Kwon, T., Lee, M.-K., Kwon, D. (eds.) ICISC 2012. LNCS, vol. 7839, pp. 495–509. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-37682-5_35
Begum, N., Nakanishi, T., Funabiki, N.: Efficient proofs for CNF formulas on attributes in pairing-based anonymous credential system. IEICE Trans. Fundam. 96-A(12), 2422–2433 (2013)
Camenisch, J., Chaabouni, R., Shelat, A.: Efficient protocols for set membership and range proofs. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 234–252. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89255-7_15
Camenisch, J., Groß, T.: Efficient attributes for anonymous credentials. In: Proceedings of the ACM Conference on Computer and Communications Security (ACM CCS 2008), pp. 345–356 (2008)
Camenisch, J., Kohlweiss, M., Soriente, C.: An accumulator based on bilinear maps and efficient revocation for anonymous credentials. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 481–500. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00468-1_27
Camenisch, J., Lysyanskaya, A.: Dynamic accumulators and application to efficient revocation of anonymous credentials. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 61–76. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45708-9_5
Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_24
Hanser, C., Slamanig, D.: Structure-preserving signatures on equivalence classes and their application to anonymous credentials. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 491–511. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45611-8_26
Izabachène, M., Libert, B., Vergnaud, D.: Block-wise P-signatures and non-interactive anonymous credentials with efficient attributes. In: Chen, L. (ed.) IMACC 2011. LNCS, vol. 7089, pp. 431–450. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25516-8_26
Sadiah, S., Nakanishi, T., Funabiki, N.: Anonymous credential system with efficient proofs for monotone formulas on attributes. In: Tanaka, K., Suga, Y. (eds.) IWSEC 2015. LNCS, vol. 9241, pp. 262–278. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22425-1_16
Sudarsono, A., Nakanishi, T., Funabiki, N.: Efficient proofs of attributes in pairing-based anonymous credential system. In: Fischer-Hübner, S., Hopper, N. (eds.) PETS 2011. LNCS, vol. 6794, pp. 246–263. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22263-4_14
Acknowledgments
This work was partially supported by JSPS KAKENHI Grant Number 19K11964.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Okishima, R., Nakanishi, T. (2019). An Anonymous Credential System with Constant-Size Attribute Proofs for CNF Formulas with Negations. In: Attrapadung, N., Yagi, T. (eds) Advances in Information and Computer Security. IWSEC 2019. Lecture Notes in Computer Science(), vol 11689. Springer, Cham. https://doi.org/10.1007/978-3-030-26834-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-26834-3_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-26833-6
Online ISBN: 978-3-030-26834-3
eBook Packages: Computer ScienceComputer Science (R0)