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Shorter identity-based encryption via asymmetric pairings

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Abstract

We present efficient identity-based encryption (IBE) under the symmetric external Diffie–Hellman (SXDH) assumption in bilinear groups; our scheme also achieves anonymity. In our IBE scheme, all parameters have constant numbers of group elements, and are shorter than those of previous constructions based on decisional linear (DLIN) assumption. Our construction uses both dual system encryption (Waters, CRYPTO 2009) and dual pairing vector spaces (Okamoto and Takashima, Pairing 2008; ASIACRYPT 2009). Specifically, we show how to adapt the recent DLIN-based instantiation of Lewko (EUROCRYPT 2012) to the SXDH assumption. To our knowledge, this is the first work to instantiate either dual system encryption or dual pairing vector spaces under the SXDH assumption. Furthermore, our work could be extended to many other functional encryption. In Particular, we show how to instantiate our framework to inner product encryption and key-policy functional encryption. All parameters of our constructions are shorter than those of DLIN-based constructions.

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Notes

  1. Here, we do not separately consider group elements from target groups of pairings, although a ciphertext typically has a group element that is from an associated target group. In Table 2, we give more accurate sizes comparing existing and our scheme.

  2. It follows from our analysis that Lewko’s IBE [26] is also anonymous, although this was not pointed out in her paper.

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Acknowledgments

We thank David Freeman, Kenny Paterson and the anonymous referees for helpful comments on an earlier draft of this paper. J. Chen, H. W. Lim, S. Ling and H. Wang are supported in part by the National Research Foundation of Singapore under Research Grant NRF-CRP2-2007-03. H. Wee is supported by NSF CAREER Award CNS-1237429.

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Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, Singapore

    Jie Chen, Hoon Wei Lim, San Ling & Huaxiong Wang

  2. George Washington University, Washington, DC, USA

    Hoeteck Wee

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  1. Jie Chen
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  2. Hoon Wei Lim
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  3. San Ling
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Correspondence to Jie Chen.

Additional information

Communicated by K. Matsuura.

A preliminary version of this paper appeared in the 5th International Conference on Pairing-Based Cryptography (Pairing 2012).

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Chen, J., Lim, H.W., Ling, S. et al. Shorter identity-based encryption via asymmetric pairings. Des. Codes Cryptogr. 73, 911–947 (2014). https://doi.org/10.1007/s10623-013-9834-3

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