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; Available format(s): PDF | BibTeX Citation Version: 20151007:031040 (All versions of this report) Short URL: ia.cr/2015/820 Discussion forum: Show discussion | Start new discussion