International Association
for Cryptologic Research

Registered attribute-based encryption (Reg-ABE), introduced by Hohenberger et.al. (Eurocrypt'23), emerges as a pivotal extension of attribute-based encryption (ABE), aimed at mitigating the key-escrow problem. Although several Reg-ABE schemes with black-box use of cryptography have been proposed so far, there remains a significant gap in the class of achievable predicates between vanilla ABE and Reg-ABE. To narrow this gap, we propose a modular framework for constructing Reg-ABE schemes for a broader class of predicates. Our framework is a Reg-ABE analog of the predicate transformation framework for ABE introduced by Attrapadung (Eurocrypt'19) and later refined by Attrapadung and Tomida (Asiacrypt'20) to function under the standard MDDH assumption. As immediate applications, our framework implies the following new Reg-ABE schemes under the standard MDDH assumption: \begin{itemize} \item the first Reg-ABE scheme for (non-)monotone span programs with the traditional completely unbounded property. \item the first Reg-ABE scheme for general non-monotone span programs (also with the completely unbounded property) as defined in the case of vanilla ABE by Attrapadung and Tomida (Asiacrypt'20). \end{itemize} Here, the term ``completely unbounded'' signifies the absence of restrictions on attribute sets for users and policies associated with ciphertexts. From a technical standpoint, we first substantially modify pair encoding schemes (PES), originally devised for vanilla ABE by Attrapadung (Eurocrypt'14), to make them compatible with Reg-ABE. Subsequently, we present a series of predicate transformations through which we can construct complex predicates, particularly those with an ``unbounded'' characteristic, starting from simple ones. Finally, we define new properties of PES necessary for constructing Reg-ABE schemes and prove that these properties are preserved through the transformations. This immediately implies that we can obtain Reg-ABE schemes for any predicates derived via predicate transformations.

At Eurocrypt'19, Attrapadung presented several transformations that dynamically compose a set of attribute-based encryption (ABE) schemes for simpler predicates into a new ABE scheme for more expressive predicates. Due to the powerful unbounded and modular nature of his compositions, many new ABE schemes can be obtained in a systematic manner (including those that resolved some open problems at the time). However, his approach heavily relies on so-called $q$-type assumptions, which are not standard. Devising such powerful compositions from standard assumptions was left as an important open problem. In this paper, we present a new framework for constructing ABE schemes that allow unbounded and dynamic predicate compositions among them, and show that the adaptive security of these composed ABE will be preserved by relying only on the standard matrix Diffie-Hellman (MDDH) assumption. This thus resolves the open problem posed by Attrapadung. As for applications, we obtain various ABEs that are the first such instantiations of their kinds from standard assumptions. These include the following adaptively secure \emph{large-universe} ABEs for Boolean formulae under MDDH: - The first completely unbounded monotone key-policy (KP)/ciphertext-policy (CP) ABE. Previously, such ABE has been only recently proposed, but only for the KP and \emph{small-universe} flavor (Kowalczyk and Wee, Eurocrypt'19). - The first completely unbounded non-monotone KP/CP-ABE. Especially, our ABEs support a new type of non-monotonicity that subsumes previous two types of non-monotonicity, namely, by Ostrovsky et al. (CCS'07) and by Okamoto and Takashima (CRYPTO'10). - The first non-monotone KP and CP-ABE with constant-size ciphertexts and secret keys, respectively. - The first monotone KP and CP-ABE with constant-size secret keys and ciphertexts, respectively. At the core of our framework lies a new \emph{partially symmetric} design of the core 1-key 1-ciphertext oracle component called Key Encoding Indistinguishability, which exploits the symmetry so as to obtain compositions.

We present a construction of an adaptively single-key secure constrained PRF (CPRF) for $$\mathbf {NC}^1$$ assuming the existence of indistinguishability obfuscation (IO) and the subgroup hiding assumption over a (pairing-free) composite order group. This is the first construction of such a CPRF in the standard model without relying on a complexity leveraging argument.To achieve this, we first introduce the notion of partitionable CPRF, which is a CPRF accommodated with partitioning techniques and combine it with shadow copy techniques often used in the dual system encryption methodology. We present a construction of partitionable CPRF for $$\mathbf {NC}^1$$ based on IO and the subgroup hiding assumption over a (pairing-free) group. We finally prove that an adaptively single-key secure CPRF for $$\mathbf {NC}^1$$ can be obtained from a partitionable CPRF for $$\mathbf {NC}^1$$ and IO.

We present several transformations that combine a set of attribute-based encryption (ABE) schemes for simpler predicates into a new ABE scheme for more expressive composed predicates. Previous proposals for predicate compositions of this kind, the most recent one being that of Ambrona et al. at Crypto’17, can be considered static (or partially dynamic), meaning that the policy (or its structure) that specifies a composition must be fixed at the setup. Contrastingly, our transformations are dynamic and unbounded: they allow a user to specify an arbitrary and unbounded-size composition policy right into his/her own key or ciphertext. We propose transformations for three classes of composition policies, namely, the classes of any monotone span programs, any branching programs, and any deterministic finite automata. These generalized policies are defined over arbitrary predicates, hence admitting modular compositions. One application from modularity is a new kind of ABE for which policies can be “nested” over ciphertext and key policies. As another application, we achieve the first fully secure completely unbounded key-policy ABE for non-monotone span programs, in a modular and clean manner, under the q-ratio assumption. Our transformations work inside a generic framework for ABE called symbolic pair encoding, proposed by Agrawal and Chase at Eurocrypt’17. At the core of our transformations, we observe and exploit an unbounded nature of the symbolic property so as to achieve unbounded-size policy compositions.

We propose new constrained pseudorandom functions (CPRFs) in traditional groups. Traditional groups mean cyclic and multiplicative groups of prime order that were widely used in the 1980s and 1990s (sometimes called “pairing free” groups). Our main constructions are as follows. We propose a selectively single-key secure CPRF for circuits with depth$$O(\log n)$$(that is,NC$$^1$$circuits) in traditional groups where n is the input size. It is secure under the L-decisional Diffie-Hellman inversion (L-DDHI) assumption in the group of quadratic residues $$\mathbb {QR}_q$$ and the decisional Diffie-Hellman (DDH) assumption in a traditional group of order qin the standard model.We propose a selectively single-key private bit-fixing CPRF in traditional groups. It is secure under the DDH assumption in any prime-order cyclic group in the standard model.We propose adaptively single-key secure CPRF for NC$$^1$$ and private bit-fixing CPRF in the random oracle model. To achieve the security in the standard model, we develop a new technique using correlated-input secure hash functions.

Attribute-based signature (ABS) schemes are advanced signature schemes that simultaneously provide fine-grained authentication while protecting privacy of the signer. Previously known expressive ABS schemes support either the class of deterministic finite automata and circuits from standard assumptions or Turing machines from the existence of indistinguishability obfuscations.In this paper, we propose the first ABS scheme for a very general policy class, all deterministic Turing machines, from a standard assumption, namely, the Symmetric External Diffie-Hellman (SXDH) assumption. We also propose the first ABS scheme that allows nondeterministic finite automata (NFA) to be used as policies. Although the expressiveness of NFAs are more restricted than Turing machines, this is the first scheme that supports nondeterministic computations as policies.Our main idea lies in abstracting ABS constructions and presenting the concept of history of computations; this allows a signer to prove possession of a policy that accepts the string associated to a message in zero-knowledge while also hiding the policy, regardless of the computational model being used. With this abstraction in hand, we are able to construct ABS for Turing machines and NFAs using a surprisingly weak NIZK proof system. Essentially we only require a NIZK proof system for proving that a (normal) signature is valid. Such a NIZK proof system together with a base signature scheme are, in turn, possible from bilinear groups under the SXDH assumption, and hence so are our ABS schemes.