Paper 2015/820

Extended Nested Dual System Groups, Revisited

Junqing Gong, Jie Chen, Xiaolei Dong, Zhenfu Cao, and Shaohua Tang

Abstract

The notion of extended nested dual system groups (ENDSG) was recently proposed by Hofheinz et al. [PKC 2015] for constructing almost-tight identity based encryptions (IBE) in the multi-instance, multi-ciphertext (MIMC) setting. However only a composite-order instantiation was proposed and more efficient prime-order instantiations are absent. The paper fills the blank by presenting two constructions. We revise the definition of ENDSG and realize it using prime-order bilinear groups based on Chen and Wee's prime-order instantiation of nested dual system groups [CRYPTO 2013]. This yields the first almost-tight IBE in the prime-order setting achieving weak adaptive security in MIMC scenario under the $d$-linear ($d$-Lin) assumption. We further enhanced the revised ENDSG to capture stronger security notions for IBE, including $B$-weak adaptive security and full adaptive security. We show that our prime-order instantiation is readily $B$-weak adaptive secure and full adaptive secure without introducing extra assumption. We then try to find better solution by fine-tuning ENDSG again and realizing it using the technique of Chen, Gay, and Wee [EUROCRYPT 2015]. This leads to an almost-tight secure IBE in the same setting with better performance than our first result, but the security relies on a non-standard assumption, $d$-linear assumption with auxiliary input ($d$-LinAI) for an even positive integer $d$. However we note that, the $2$-LinAI assumption is implied by the external decisional linear (XDLIN) assumption. This concrete instantiation could also be realized using symmetric bilinear groups under standard decisional linear assumption.

Metadata
Available format(s)
PDF
Publication info
Preprint. MINOR revision.
Keywords
Identity based encryptionsDual system groupsTight securitySecurity modelPrime-order bilinear groups
Contact author(s)
gongjunqing @ 126 com
S080001 @ e ntu edu sg
History
2015-10-07: revised
2015-08-21: received
See all versions
Short URL
https://ia.cr/2015/820
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/820,
      author = {Junqing Gong and Jie Chen and Xiaolei Dong and Zhenfu Cao and Shaohua Tang},
      title = {Extended Nested Dual System Groups, Revisited},
      howpublished = {Cryptology ePrint Archive, Paper 2015/820},
      year = {2015},
      note = {\url{https://eprint.iacr.org/2015/820}},
      url = {https://eprint.iacr.org/2015/820}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.