Cryptology ePrint Archive: Report 2015/820

Extended Nested Dual System Groups, Revisited

Junqing Gong and Jie Chen and Xiaolei Dong and 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.

Category / Keywords: Identity based encryptions, Dual system groups, Tight security, Security model, Prime-order bilinear groups

Date: received 20 Aug 2015, last revised 6 Oct 2015

Contact author: gongjunqing at 126 com; S080001@e ntu edu sg;

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Version: 20151007:031040 (All versions of this report)

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