# Making **Any** Identity-Based Encryption Accountable, Efficiently

**Any**

## Abstract

Identity-Based Encryption (IBE) provides a compelling solution to the PKI management problem, however it comes with the serious privacy consideration that a trusted party (called the PKG) is required to generate (and hence also know) the secret keys of all users. This inherent key escrow problem is considered to be one of the major reasons hindering the wider utilization of IBE systems. In order to address this problem, Goyal [20] introduced the notion of accountable authority IBE (A-IBE), in which a judge can differentiate the PKG from the user as the source of a decryption software. Via this “tracing” mechanism, A-IBE deters the PKG from leaking the user’s secret key and hence offers a defense mechanism for IBE users against a malicious PKG.

All previous works on A-IBE focused on specialized constructions trying to achieve different properties and efficiency enhancements. In this paper for the first time we show how to add accountability to *any* IBE scheme using oblivious transfer (OT), with almost the same ciphertext efficiency as the underlying IBE. Furthermore, we extend our generic construction to support identity reuse without losing efficiency. This property is desirable in practice as users may accidentally lose their secret keys and they -naturally- prefer not to abandon their identities. How to achieve this property was open until our work. Along the way, we first modify the generic construction and develop a new technique to provide public traceability generically.

## Notes

### Acknowledgements.

We thank Hong-Sheng Zhou for the early discussions. We thank the anonymous reviewer to point out the simplification for S-I. The authors were supported by the ERC project CODAMODA.

## References

- 1.Al-Riyami, S.S., Paterson, K.G.: Certificateless public key cryptography. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 452–473. Springer, Heidelberg (2003) CrossRefGoogle Scholar
- 2.Au, M.H., Huang, Q., Liu, J.K., Susilo, W., Wong, D.S., Yang, G.: Traceable and retrievable identity-based encryption. In: Bellovin, S.M., Gennaro, R., Keromytis, A.D., Yung, M. (eds.) ACNS 2008. LNCS, vol. 5037, pp. 94–110. Springer, Heidelberg (2008) CrossRefGoogle Scholar
- 3.Bellare, M., Micali, S.: Non-interactive oblivious transfer and applications. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 547–557. Springer, Heidelberg (1989) Google Scholar
- 4.Bellare, M., Rogaway, P.: Random oracles are practical: Aa paradigm for designing efficient protocols. In: ACM Conference on Computer and Communications Security, pp. 62–73 (1993)Google Scholar
- 5.Boneh, D., Boyen, X.: Efficient selective-ID secure identity-based encryption without random oracles-. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004) CrossRefGoogle Scholar
- 6.Boneh, D., Boyen, X.: Secure identity based encryption without random oracles. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 443–459. Springer, Heidelberg (2004) CrossRefGoogle Scholar
- 7.Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004) CrossRefGoogle Scholar
- 8.Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, p. 213. Springer, Heidelberg (2001) CrossRefGoogle Scholar
- 9.Boneh, D., Halevi, S., Hamburg, M., Ostrovsky, R.: Circular-secure encryption from decision Diffie-Hellman. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 108–125. Springer, Heidelberg (2008) CrossRefGoogle Scholar
- 10.Boneh, D., Naor, M.: Traitor tracing with constant size ciphertext. In: ACM Conference on Computer and Communications Security, pp. 501–510 (2008)Google Scholar
- 11.Boneh, D., Sahai, A., Waters, B.: Functional encryption: definitions and challenges. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 253–273. Springer, Heidelberg (2011) CrossRefGoogle Scholar
- 12.Boyen, X., Martin, L.: Identity-Based Cryptography Standard (IBCS) #1: Supersingular Curve Implementations of the BF and BB1 Cryptosystems. RFC 5091 (Informational), December (2007)Google Scholar
- 13.Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptol.
**13**(1), 143–202 (2000)MathSciNetCrossRefGoogle Scholar - 14.Chow, S.S.M.: Removing escrow from identity-based encryption. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 256–276. Springer, Heidelberg (2009) CrossRefGoogle Scholar
- 15.Cramer, R., Damgåard, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994) Google Scholar
- 16.Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987) Google Scholar
- 17.Gamal, T.E.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory
**31**(4), 469–472 (1985)MathSciNetCrossRefGoogle Scholar - 18.Gentry, C.: Certificate-based encryption and the certificate revocation problem. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 272–293. Springer, Heidelberg (2003) CrossRefGoogle Scholar
- 19.Gentry, C.: Practical identity-based encryption without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006) CrossRefGoogle Scholar
- 20.Goyal, V.: Reducing trust in the PKG in identity based cryptosystems. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 430–447. Springer, Heidelberg (2007) CrossRefGoogle Scholar
- 21.Goyal, V., Lu, S., Sahai, A., Waters, B.: Black-box accountable authority identity-based encryption. In: ACM Conference on Computer and Communications Security, pp. 427–436 (2008)Google Scholar
- 22.Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM Conference on Computer and Communications Security, pp. 89–98 (2006)Google Scholar
- 23.Guruswami, V., Indyk, P.: Expander-based constructions of efficiently decodable codes. FOCS
**2001**, 658–667 (2001)MathSciNetGoogle Scholar - 24.Kiayias, A., Tang, Q.: How to keep a secret: leakage deterring public-key cryptosystems. In: ACM Conference on Computer and Communications Security, pp. 943–954 (2013)Google Scholar
- 25.Lai, J., Deng, R.H., Zhao, Y., Weng, J.: Accountable authority identity-based encryption with public traceability. In: Dawson, E. (ed.) CT-RSA 2013. LNCS, vol. 7779, pp. 326–342. Springer, Heidelberg (2013) CrossRefGoogle Scholar
- 26.Libert, B., Vergnaud, D.: Towards black-box accountable authority ibe with short ciphertexts and private keys. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 235–255. Springer, Springer (2009) CrossRefGoogle Scholar
- 27.Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: SODA, pp. 448–457 (2001)Google Scholar
- 28.Sahai, A., Seyalioglu, H.: Fully secure accountable-authority identity-based encryption. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 296–316. Springer, Heidelberg (2011) CrossRefGoogle Scholar
- 29.Sahai, A., Waters, B.: Fuzzy Identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005) CrossRefGoogle Scholar
- 30.Schnorr, C.-P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990) Google Scholar
- 31.Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985) Google Scholar
- 32.Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005) CrossRefGoogle Scholar
- 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) CrossRefGoogle Scholar
- 34.Yuen, T.H., Chow, S.S.M., Zhang, C., Yiu, S.-M.: Exponent-inversion signatures and ibe under static assumptions. IACR Cryptol. ePrint Arch.
**2014**, 311 (2014)Google Scholar

## Copyright information

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (http://creativecommons.org/licenses/by-nc/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.