Doubly Spatial Encryption from DBDH

Functional encryption is an emerging paradigm for public-key encryption which enables fine-grained control of access to encrypted data. Doubly-spatial encryption (DSE) captures all functionalities that we know how to realize via pairings-based assumptions, including (H)IBE, IPE, NIPE, CP-ABE and KP-ABE. In this paper, we propose a construction of DSE from the decisional bilinear Diffie-Hellman (DBDH) assumption. This also yields the first non-zero inner product encryption (NIPE) scheme based on DBDH. Quite surprisingly, we know how to realize NIPE and DSE from stronger assumptions in bilinear groups but not from the basic DBDH assumption. Along the way, we present a novel algebraic characterization of *NO* instances for the DSE functionality, which we use crucially in the proof of security

Fully Secure (Doubly-)Spatial Encryption under Simpler Assumptions

Spatial encryption was first proposed by Boneh and Hamburg in 2008. It is one implementation of the generalized identity-based encryption schemes and many systems with a variety of properties can be derived from it. Recently, Hamburg improved the notion by presenting a variant called doubly-spatial encryption. The doubly spatial encryption is more powerful and expressive. More useful cryptography systems can be builded from it, such as attribute-based encryption, etc. However, most presented spatial encryption schemes are proven to be selectively secure. Only a few spatial encryption schemes achieve adaptive security, but not under standard assumptions. And no fully secure doubly-spatial encryption scheme has been presented before. In this paper, we primarily focus on the adaptive security of (doubly-)spatial encryption. A spatial encryption scheme and a doubly-spatial encryption scheme have been proposed. Then we apply the dual system methodology proposed by Waters in the security proof. Both of the schemes can be proven adaptively secure under standard assumptions, the decisional linear (DLIN) assumption and the decisional bilinear Diffie-Hellman (DBDH) assumption, over prime order groups in the standard model. To the best of our knowledge, our second scheme is the first fully secure construction of doubly-spatial encryption

Generic Conversions from CPA to CCA secure Functional Encryption

In 2004, Canetti-Halevi-Katz and later Boneh-Katz showed generic CCA-secure PKE constructions from a CPA-secure IBE. Goyal et al. in 2006 further extended the aforementioned idea implicitly to provide a specific CCA-secure KP-ABE with policies represented by monotone access trees. Later, Yamada et al. in 2011 generalized the CPA to CCA conversion to all those ABE, where the policies are represented by either monotone access trees (MAT) or monotone span programs (MSP), but not the others like sets of minimal sets. Moreover, the underlying CPA-secure constructions must satisfy one of the two features called key-delegation and verifiability. Along with ABE, many other different encryptions schemes, such as inner-product, hidden vector, spatial encryption schemes etc. can be studied under an unified framework, called functional encryption (FE), as introduced by Boneh-Sahai-Waters in 2011. The generic conversions, due to Yamada et al., can not be applied to all these functional encryption schemes. On the other hand, to the best of our knowledge, there is no known CCA-secure construction beyond ABE over MSP and MAT. This paper provides different ways of obtaining CCA-secure functional encryptions of almost all categories. In particular, we provide a generic conversion from a CPA-secure functional encryption into a CCA-secure functional encryption provided the underlying CPA-secure encryption scheme has either restricted delegation or verifiability feature. We observe that almost all functional encryption schemes have this feature. The KP-FE schemes of Waters (proposed in 2012) and Attrapadung (proposed in 2014) for regular languages do not possess the usual delegation property. However, they can be converted into corresponding CCA-secure schemes as they satisfy the restricted delegation

Fully Secure Spatial Encryption under Simple Assumptions with Constant-Size Ciphertexts

In this paper, we propose two new spatial encryption (SE) schemes based on existing inner product encryption (IPE) schemes. Both of our SE schemes are fully secure under simple assumptions and in prime order bilinear groups. Moreover, one of our SE schemes has constant-size ciphertexts. Since SE implies hierarchical identity-based encryption (HIBE), we also obtain a fully secure HIBE scheme with constant-size ciphertexts under simple assumptions. Our second SE scheme is attribute-hiding (or anonymous). It has sizes of public parameters, secret keys and ciphertexts that are quadratically smaller than the currently known SE scheme with similar properties. As a side result, we show that negated SE is equivalent to non-zero IPE. This is somewhat interesting since the latter is known to be a special case of the former