ABE with Tag Made Easy: Concise Framework and New Instantiations in Prime-order Groups

Among all existing identity-based encryption (IBE) schemes in the bilinear group, Wat-IBE proposed by Waters [CRYPTO, 2009] and JR-IBE proposed by Jutla and Roy [AsiaCrypt, 2013] are quite special. A secret key and/or ciphertext in these two schemes consist of several group elements and an integer which is usually called tag. A series of prior work was devoted to extending them towards more advanced attribute-based encryption (ABE) including inner-product encryption (IPE), hierarchical IBE (HIBE). Recently, Kim et al. [SCN, 2016] introduced the notion of tag-based encoding and presented a generic framework for extending Wat-IBE. We may call these ABE schemes ABE with tag or tag-based ABE. Typically, a tag-based ABE construction is more efficient than its counterpart without tag. However the research on tag-based ABE severely lags—We do not know how to extend JR-IBE in a systematic way and there is no tag-based ABE for boolean span program even with Kim et al.’s generic framework. In this work, we proposed a generic framework for tag-based ABE which is based on JR-IBE and compatible with Chen et al.’s (attributehiding) predicate encoding [EuroCrypt, 2015]. The adaptive security in the standard model relies on the k-linear assumption in the asymmetric prime-order bilinear group. This is the first framework showing how to extend JR-IBE systematically. In fact our framework and its simple extension are able to cover most concrete tag-based ABE constructions in previous literature. Furthermore, since Chen et al.’s predicate encoding supports a large number of predicates including boolean span program, we can now give the first (both key-policy and ciphertext-policy) tagbased ABE for boolean span program in the standard model. Technically our framework is based on a simplified version of JR-IBE. Both the description and its proof are quite similar to the prime-order IBE derived ? School of Computer Science and Software Engineering. Supported by the National Natural Science Foundation of China (Nos. 61472142, 61632012) and the Science and Technology Commission of Shanghai Municipality (No. 14YF1404200). Homepage: http://www.jchen.top ?? Partially supported by the French ANR ALAMBIC project (ANR-16-CE39-0006). from Chen et al.’s framework. This not only allows us to work with Chen et al.’s predicate encoding but also provides us with a clear explanation of JR-IBE and its proof technique.