Multi-Client Inner Product Encryption: Function-Hiding Instantiations Without Random Oracles

In a Multi-Client Functional Encryption (MCFE) scheme, $n$ clients each obtain a secret encryption key from a trusted authority. During each time step $t$, each client $i$ can encrypt its data using its secret key. The authority can use its master secret key to compute a functional key given a function $f$, and the functional key can be applied to a collection of $n$ clients’ ciphertexts encrypted to the same time step, resulting in the outcome of $f$ on the clients’ data. In this paper, we focus on MCFE for inner-product computations. If an MCFE scheme hides not only the clients’ data, but also the function $f$, we say it is function hiding. Although MCFE for inner-product computation has been extensively studied, how to achieve function privacy is still poorly understood. The very recent work of Agrawal et al. showed how to construct a function-hiding MCFE scheme for inner-product assuming standard bilinear group assumptions; however, they assume the existence of a random oracle and prove only a relaxed, selective security notion. An intriguing open question is whether we can achieve function-hiding MCFE for inner-product without random oracles. In this work, we are the first to show a function-hiding MCFE scheme for inner products, relying on standard bilinear group assumptions. Further, we prove adaptive security without the use of a random oracle. Our scheme also achieves succinct ciphertexts, that is, each coordinate in the plaintext vector encrypts to only $O(1$) group elements. Our main technical contribution is a new upgrade from single-input functional encryption for inner-products to a multi-client one. Our upgrade preserves function privacy, that is, if the original single-input scheme is function-hiding, so is the resulting multi-client construction. Further, this new upgrade allows us to obtain a conceptually simple construction

Multi-Client Functional Encryption for Separable Functions

In this work, we provide a compiler that transforms a single-input functional encryption scheme for the class of polynomially bounded circuits into a multi-client functional encryption (MCFE) scheme for the class of separable functions. An n-input function f is called separable if it can be described as a list of polynomially bounded circuits f^1, ... , f^n s.t. f(x_1, ... , x_n)= f^1(x_1)+ ... + f^n(x_n) for all x_1 ,... , x_n. Our compiler extends the works of Brakerski et al. [Eurocrypt 2016] and of Komargodski et al. [Eurocrypt 2017] in which a generic compiler is proposed to obtain multi-input functional encryption (MIFE) from single-input functional encryption. Our construction achieves the stronger notion of MCFE but for the less generic class of separable functions. Prior to our work, a long line of results has been proposed in the setting of MCFE for the inner-product functionality, which is a special case of a separable function. We also propose a modified version of the notion of decentralized MCFE introduced by Chotard et al. [Asiacrypt 2018] that we call outsourceable mulit-client functional encryption (OMCFE). Intuitively, the notion of OMCFE makes it possible to distribute the load of the decryption procedure among at most n different entities, which will return decryption shares that can be combined (e.g., additively) thus obtaining the output of the computation. This notion is especially useful in the case of a very resource consuming decryption procedure, while the combine algorithm is non-time consuming. We also show how to extend the presented MCFE protocol to obtain an OMCFE scheme for the same functionality class

Multi-Client Functional Encryption with Fine-Grained Access Control

International audienceMulti-Client Functional Encryption (MCFE) and Multi-Input Functional Encryption (MIFE) are very interesting extensions of Functional Encryption for practical purpose. They allow to compute joint function over data from multiple parties. Both primitives are aimed at applications in multiuser settings where decryption can be correctly output for users with appropriate functional decryption keys only. While the definitions for a single user or multiple users were quite general and can be realized for general classes of functions as expressive as Turing machines or all circuits, efficient schemes have been proposed so far for concrete classes of functions: either only for access control, i.e. the identity function under some conditions, or linear/quadratic functions under no condition. In this paper, we target classes of functions that explicitly combine some evaluation functions independent of the decrypting user under the condition of some access control. More precisely, we introduce a framework for MCFE with fine-grained access control and propose constructions for both single-client and multi-client settings, for inner-product evaluation and access control via Linear Secret Sharing Schemes (LSSS), with selective and adaptive security. The only known work that combines functional encryption in multiuser setting with access control was proposed by Abdalla et al. (Asiacrypt '20), which relies on a generic transformation from the single-client schemes to obtain MIFE schemes that suffer a quadratic factor of n (where n denotes the number of clients) in the ciphertext size. We follow a different path, via MCFE: we present a duplicate-and-compress technique to transform the single-client scheme and obtain a MCFE with fine-grained access control scheme with only a linear factor of n in the ciphertext size. Our final scheme thus outperforms the Abdalla et al.'s scheme by a factor n, as one can obtain MIFE from MCFE by making all the labels in MCFE a fixed public constant. The concrete constructions are secure under the SXDH assumption, in the random oracle model for the MCFE scheme, but in the standard model for the MIFE improvement

Ad Hoc Multi-Input Functional Encryption

Consider sources that supply sensitive data to an aggregator. Standard encryption only hides the data from eavesdroppers, but using specialized encryption one can hope to hide the data (to the extent possible) from the aggregator itself. For flexibility and security, we envision schemes that allow sources to supply encrypted data, such that at any point a dynamically-chosen subset of sources can allow an agreed-upon joint function of their data to be computed by the aggregator. A primitive called multi-input functional encryption (MIFE), due to Goldwasser et al. (EUROCRYPT 2014), comes close, but has two main limitations: - it requires trust in a third party, who is able to decrypt all the data, and - it requires function arity to be fixed at setup time and to be equal to the number of parties. To drop these limitations, we introduce a new notion of ad hoc MIFE. In our setting, each source generates its own public key and issues individual, function-specific secret keys to an aggregator. For successful decryption, an aggregator must obtain a separate key from each source whose ciphertext is being computed upon. The aggregator could obtain multiple such secret-keys from a user corresponding to functions of varying arity. For this primitive, we obtain the following results: - We show that standard MIFE for general functions can be bootstrapped to ad hoc MIFE for free, i.e. without making any additional assumption. - We provide a direct construction of ad hoc MIFE for the inner product functionality based on the Learning with Errors (LWE) assumption. This yields the first construction of this natural primitive based on a standard assumption. At a technical level, our results are obtained by combining standard MIFE schemes and two-round secure multiparty computation (MPC) protocols in novel ways highlighting an interesting interplay between MIFE and two-round MPC

Decentralizing Inner-Product Functional Encryption

International audienceMulti-client functional encryption (MCFE) is a more flexible variant of functional encryption whose functional decryption involves multiple ciphertexts from different parties. Each party holds a different secret key and can independently and adaptively be corrupted by the adversary. We present two compilers for MCFE schemes for the inner-product functionality, both of which support encryption labels. Our first compiler transforms any scheme with a special key-derivation property into a decentralized scheme, as defined by Chotard et al. (ASIACRYPT 2018), thus allowing for a simple distributed way of generating functional decryption keys without a trusted party. Our second compiler allows to lift an unnatural restriction present in existing (decentralized) MCFE schemes, which requires the adversary to ask for a ciphertext from each party. We apply our compilers to the works of Abdalla et al. (CRYPTO 2018) and Chotard et al. (ASIACRYPT 2018) to obtain schemes with hitherto unachieved properties. From Abdalla et al., we obtain instantiations of DMCFE schemes in the standard model (from DDH, Paillier, or LWE) but without labels. From Chotard et al., we obtain a DMCFE scheme with labels still in the random oracle model, but without pairings

Equivalence-based Security for Querying Encrypted Databases: Theory and Application to Privacy Policy Audits

Motivated by the problem of simultaneously preserving confidentiality and usability of data outsourced to third-party clouds, we present two different database encryption schemes that largely hide data but reveal enough information to support a wide-range of relational queries. We provide a security definition for database encryption that captures confidentiality based on a notion of equivalence of databases from the adversary's perspective. As a specific application, we adapt an existing algorithm for finding violations of privacy policies to run on logs encrypted under our schemes and observe low to moderate overheads.Comment: CCS 2015 paper technical report, in progres