(Compact) Adaptively Secure FE for Attribute-Weighted Sums from k-Lin

This paper presents the first adaptively simulation secure functional encryption (FE) schemes for attribute-weighted sums. In such an FE scheme, encryption takes as input N pairs of attribute {(x_i, z_i )}_{i \in [N]} for some N \in \mathbb{N} where the attributes {x_i}_{i \in [N]} are public while the attributes {z_i}_{i \in [N]} are private. The indices i \in [N] are referred to as the slots. A secret key corresponds to some weight function f, and decryption recovers the weighted sum \sum_{i \in [N]} f(x_i)z_i. This is an important functionality with a wide range of potential real life applications. In the proposed FE schemes attributes are viewed as vectors and weight functions are arithmetic branching programs (ABP). We present two schemes with varying parameters and levels of adaptive security. (a) We first present a one-slot scheme that achieves adaptive security in the simulation-based security model against a bounded number of ciphertext queries and an arbitrary polynomial number of secret key queries both before and after the ciphertext queries. This is the best possible level of security one can achieve in the adaptive simulation-based framework. From the relations between the simulation-based and indistinguishability-based security frameworks for FE, it follows that the proposed FE scheme also achieves indistinguishability- based adaptive security against an a-priori unbounded number of ciphertext queries and an arbitrary polynomial number of secret key queries both before and after the ciphertext queries. Moreover, the scheme enjoys compact ciphertexts that do not grow with the number of appearances of the attributes within the weight functions. (b) Next, bootstrapping from the one-slot scheme, we present an unbounded-slot scheme that achieves simulation-based adaptive security against a bounded number of ciphertext and pre-ciphertext secret key queries while supporting an a-priori unbounded number of post-ciphertext secret key queries. The scheme achieves public parameters and secret key sizes independent of the number of slots N and a secret key can decrypt a ciphertext for any a-priori unbounded N. Further, just like the one-slot scheme, this scheme also has the ciphertext size independent of the number of appearances of the attributes within the weight functions. However, all the parameters of the scheme, namely, the master public key, ciphertexts, and secret keys scale linearly with the bound on the number of pre-ciphertext secret key queries. Our schemes are built upon asymmetric bilinear groups of prime order and the security is derived under the standard (bilateral) k-Linear (k-Lin) assumption. Our work resolves an open problem posed by Abdalla, Gong, and Wee in CRYPTO 2020, where they presented an unbounded-slot FE scheme for attribute-weighted sum achieving only semi-adaptive simulation security. At a technical level, our work extends the recent adaptive security framework of Lin and Luo [EUROCRYPT 2020], devised to achieve compact ciphertexts in the context of indistinguishability-based payload-hiding security, into the setting of simulation-based adaptive attribute-hiding security

Registration-Based Functional Encryption

This paper introduces registered functional encryption (RFE) that eliminates trust on the central authority for handling secrets. Unlike standard functional encryption (FE), in an RFE scheme, users create their secret keys themselves and then register the associated public keys to a key curator along with the functions they wish to compute on the encrypted data. The key curator aggregates the public keys from the different users into a single compact master public key. To decrypt, users occasionally need to obtain helper decryption keys from the key curator which they combine with their own secret keys. We require that the size of the aggregated public key, the helper decryption keys, the ciphertexts, as well as the encryption/decryption time to be polylogarithmic in the number of registered users. Moreover, the key curator is entirely transparent and maintains no secrets. RFE generalizes the notions of registration-based encryption (RBE) introduced by Garg et al. (TCC 2018) and registered attribute-based encryption introduced by Hohenberger et al. (EUROCRYPT 2023) who dealt with the “all-or-nothing” variants of FE. We present an RFE scheme for general functions and an arbitrary number of users from indistinguishability obfuscation and somewhere statistically binding hash functions. Surprisingly, our construction is achieved via only a minor tweak applied to the registered ABE of Hohenberger et al

Decentralized Multi-Authority Attribute-Based Inner-Product FE: Large Universe and Unbounded

This paper presents the first decentralized multi-authority attribute-based inner product functional encryption (MA-ABIPFE) schemes supporting vectors of a priori unbounded lengths. The notion of AB-IPFE, introduced by Abdalla et al. [ASIACRYPT 2020], combines the access control functionality of attribute-based encryption (ABE) with the possibility of evaluating linear functions on encrypted data. A decentralized MA-ABIPFE defined by Agrawal et al. [TCC 2021] essentially enhances the ABE component of AB-IPFE to the decentralized multi-authority setting where several authorities can independently issue user keys involving attributes under their control. In MA-ABIPFE for unbounded vectors (MA-ABUIPFE), encryptors can encrypt vectors of arbitrary length under access policies of their choice whereas authorities can issue secret keys to users involving attributes under their control and vectors of arbitrary lengths. Decryption works in the same way as for MA-ABIPFE provided the lengths of the vectors within the ciphertext and secret keys match. We present two MA-ABUIPFE schemes supporting access policies realizable by linear secret sharing schemes (LSSS), in the significantly faster prime-order bilinear groups under decisional assumptions based on the target groups which are known to be weaker compared to their counterparts based in the source groups. The proposed schemes demonstrate different trade-offs between versatility and underlying assumptions. The first scheme allows each authority to control a bounded number of attributes and is proven secure under the well-studied decisional bilinear Diffie-Hellman (DBDH) assumption. On the other hand, the second scheme allows authorities to control exponentially many attributes, that is, supports large attribute universe, and is proven secure under a non-interactive q-type variant of the DBDH assumption called L-DBDH, similar to what was used in prior large-universe multi-authority ABE (MA-ABE) construction. When compared with the only known MA-ABIPFE scheme due to Agrawal et al. [TCC 2021], our schemes offer significantly higher efficiency while offering greater flexibility and security under weaker assumptions at the same time. Moreover, unlike Agrawal et al., our schemes can support the appearance of the same attributes within an access policy arbitrarily many times. Since efficiency and practicality is the prime focus of this work, we prove the security of our constructions in the random oracle model against static adversaries similar to prior works on MA-ABE with similar motivations and assumptions. On the technical side, we extend the unbounded IPFE techniques of Dufour-Sans and Pointcheval [ACNS 2019] to the context of MA-ABUIPFE by introducing a novel hash-decomposition technique

Functional Encryption for Inner Product with Full Function Privacy

Functional encryption (FE) supports constrained decryption keys that allow decrypters to learn specific functions of encrypted messages. In numerous practical applications of FE, confidentiality must be assured not only for the encrypted data but also for the functions for which functional keys are provided. This paper presents a non-generic simple private key FE scheme for the inner product functionality, also known as inner product encryption (IPE). In contrast to the existing similar schemes, our construction achieves the strongest indistinguishability-based notion of function privacy in the private key setting without employing any computationally expensive cryptographic tool or non-standard complexity assumption. Our construction is built in the asymmetric bilinear pairing group setting of prime order. The security of our scheme is based on the well-studied Symmetric External Diffie-Hellman (SXDH) assumption

Full-Hiding (Unbounded) Multi-Input Inner Product Functional Encryption from the kk-Linear Assumption

This paper presents two non-generic and practically efficient private key multi-input functional encryption (MIFE) schemes for the multi-input version of the inner product functionality that are the first to achieve simultaneous message and function privacy, namely, the full-hiding security for a non-trivial multi-input functionality under well-studied cryptographic assumptions. Our MIFE schemes are built in bilinear groups of prime order, and their security is based on the standard $k$-Linear ($k$-LIN) assumption (along with the existence of semantically secure symmetric key encryption and pseudorandom functions). Our constructions support polynomial number of encryption slots (inputs) without incurring any super-polynomial loss in the security reduction. While the number of encryption slots in our first scheme is apriori bounded, our second scheme can withstand an arbitrary number of encryption slots. Prior to our work, there was no known MIFE scheme for a non-trivial functionality, even without function privacy, that can support an unbounded number of encryption slots without relying on any heavy-duty building block or little-understood cryptographic assumption

Decentralized Multi-Authority ABE for DNFs from LWE

We construct the first decentralized multi-authority attribute-based encryption (MA-ABE) scheme for a non-trivial class of access policies whose security is based (in the random oracle model) solely on the Learning With Errors (LWE) assumption. The supported access policies are ones described by DNF formulas. All previous constructions of MA-ABE schemes supporting any non-trivial class of access policies were proven secure (in the random oracle model) assuming various assumptions on bilinear maps. In our system, any party can become an authority and there is no requirement for any global coordination other than the creation of an initial set of common reference parameters. A party can simply act as a standard ABE authority by creating a public key and issuing private keys to different users that reflect their attributes. A user can encrypt data in terms of any DNF formulas over attributes issued from any chosen set of authorities. Finally, our system does not require any central authority. In terms of efficiency, when instantiating the scheme with a global bound $s$ on the size of access policies, the sizes of public keys, secret keys, and ciphertexts, all grow with $s$. Technically, we develop new tools for building ciphertext-policy ABE (CP-ABE) schemes using LWE. Along the way, we construct the first provably secure CP-ABE scheme supporting access policies in $\mathsf{NC}^1$ that avoids the generic universal-circuit-based key-policy to ciphertext-policy transformation. In particular, our construction relies on linear secret sharing schemes with new properties and in some sense is more similar to CP-ABE schemes that rely on bilinear maps. While our CP-ABE construction is not more efficient than existing ones, it is conceptually intriguing and further we show how to extend it to get the MA-ABE scheme described above

Decentralized Multi-Authority ABE for NC^1 from Computational-BDH

Decentralized multi-authority attribute-based encryption (-) is a strengthening of standard ciphertext-policy attribute-based encryption so that there is no trusted central authority: any party can become an authority and there is no requirement for any global coordination other than the creation of an initial set of common reference parameters. Essentially, any party can act as an authority for some attribute by creating a public key of its own and issuing private keys to different users that reflect their attributes. This paper presents the first - proven secure under the standard search variant of bilinear Diffie-Hellman (CBDH) and in the random oracle model. Our scheme supports all access policies captured by 1 circuits. All previous constructions were proven secure in the random oracle model and additionally were based on decision assumptions such as the DLIN assumption, non-standard -type assumptions, or subspace decision assumptions over composite-order bilinear groups

General Circuit Realizing Compact Revocable Attribute-Based Encryption from Multilinear Maps

This paper demonstrates new technique for managing revocation in the context of attribute-based encryption (ABE) and presents two selectively secure directly revocable ABE (RABE) constructions – supporting decryption policies realizable by polynomial size Boolean circuits of arbitrary fan-out and – featuring compactness in the sense that the number of revocation controlling components in ciphertexts and decryption keys are constant. In fact, our RABE schemes are the first to achieve these parameters. Both our constructions utilize multilinear maps. The size of public parameter in our first construction is linear to the maximum number of users supported by the system while in the second construction we reduce it to logarithmic

Short Attribute-Based Signatures for Arbitrary Turing Machines from Standard Assumptions

This paper presents the first attribute-based signature (ABS) scheme supporting signing policies representable by Turing machines (TM), based on well-studied computational assumptions. Our work supports arbitrary TMs as signing policies in the sense that the TMs can accept signing attribute strings of unbounded polynomial length and there is no limit on their running time, description size, or space complexity. Moreover, we are able to achieve input-specific running time for the signing algorithm. All other known expressive ABS schemes could at most support signing policies realizable by either arbitrary polynomial-size circuits or TMs having a pre-determined upper bound on the running time. Consequently, those schemes can only deal with signing attribute strings whose lengths are a priori bounded, as well as suffers from the worst-case running time problem. On a more positive note, for the first time in the literature, the signature size of our ABS scheme only depends on the size of the signed message and is completely independent of the size of the signing policy under which the signature is generated. This is a significant achievement from the point of view of communication efficiency. Our ABS construction makes use of indistinguishability obfuscation (IO) for polynomial-size circuits and certain IO-compatible cryptographic tools. Note that, all of these building blocks including IO for polynomial-size circuits are currently known to be realizable under well-studied computational assumptions

Succinct Predicate and Online-Offline Multi-Input Inner Product Encryptions under Standard Static Assumptions

This paper presents expressive predicate encryption (PE) systems, namely non-zero inner-product-predicate encryption (NIPPE) and attribute-based encryption (ABE) supporting monotone span programs achieving best known parameters among existing similar schemes under well-studied static complexity assumptions. Both the constructions are built in composite order bilinear group setting and involve only 2 group elements in the ciphertexts. More interestingly, our NIPPE scheme, which additionally features only 1 group element in the decryption keys, is the first to attain succinct ciphertexts and decryption keys simultaneously. For proving selective security of these constructions under the Subgroup Decision assumptions, which are the most standard static assumptions in composite order bilinear group setting, we apply the extended version of the elegant D´ej`a Q framework, which was originally proposed as a general technique for reducing the q-type complexity assumptions to their static counter parts. Our work thus demonstrates the power of this framework in overcoming the need of q-type assumptions, which are vulnerable to serious practical attacks, for deriving security of highly expressive PE systems with compact parameters. We further introduce the concept of online-offline multi-input functional encryption (OO-MIFE), which is a crucial advancement towards realizing this highly promising but computationally intensive cryptographic primitive in resource bounded and power constrained devices. We also instantiate our notion of OO-MIFE by constructing such a scheme for the multi-input analog of the inner product functionality, which has a wide range of application in practice. Our OO-MIFE scheme for multiinput inner products is built in asymmetric bilinear groups of prime order and is proven selectively secure under the well-studied k-Linear (k-LIN) assumption