Bounded-Collusion Attribute-Based Encryption from Minimal Assumptions

Attribute-based encryption (ABE) enables encryption of messages under access policies so that only users with attributes satisfying the policy can decrypt the ciphertext. In standard ABE, an arbitrary number of colluding users, each without an authorized attribute set, cannot decrypt the ciphertext. However, all existing ABE schemes rely on concrete cryptographic assumptions such as the hardness of certain problems over bilinear maps or integer lattices. Furthermore, it is known that ABE cannot be constructed from generic assumptions such as public-key encryption using black-box techniques. In this work, we revisit the problem of constructing ABE that tolerates collusions of arbitrary but a priori bounded size. We present an ABE scheme secure against bounded collusions that requires only semantically secure public-key encryption. Our scheme achieves significant improvement in the size of the public parameters, secret keys, and ciphertexts over the previous construction of bounded-collusion ABE from minimal assumptions by Gorbunov et al. (CRYPTO 2012). We also obtain bounded-collusion symmetric-key ABE (which requires the secret key for encryption) by replacing the public-key encryption with symmetric-key encryption, which can be built from the minimal assumption of one-way functions

Functional Encryption for Bounded Collusions, Revisited

We provide a new construction of functional encryption (FE) for circuits in the bounded collusion model. In this model, security of the scheme is guaranteed as long as the number of colluding adversaries can be a-priori bounded by some polynomial q . Our construction supports arithmetic circuits as against Boolean circuits, which have been the focus of all prior work. The ciphertext of our scheme is sublinear in the circuit size for the circuit class NC_1 when based on Ring LWE and any constant depth when based on standard LWE. This gives the first constructions of arithmetic reusable garbled circuits. Additionally, our construction achieves several desirable features: • Our construction for reusable garbled circuits for NC 1 achieves the optimal “full” simulation based security. • When generalised to handle Q queries for any fixed polynomial Q, our ciphertext size grows additively with Q^2 . Such query dependence on ciphertext size has only been achieved in a weaker security game otherwise [Agr17]. • The ciphertext of our scheme can be divided into a succinct data dependent component and a non-succinct data independent component. This makes it well suited for optimization in an online-offline model that allows a majority of the computation to be performed in an offline phase, before the data becomes available. Security of our scheme may be based on the Learning With Errors assumption (LWE) or its ring variant (Ring-LWE). To achieve our result, we provide new public key and ciphertext evaluation algorithms in the context of functional encryption. These algorithms are general, and may find application elsewhere

Dynamic Collusion Bounded Functional Encryption from Identity-Based Encryption

Functional Encryption is a powerful notion of encryption in which each decryption key is associated with a function $f$ such that decryption recovers the function evaluation $f(m)$. Informally, security states that a user with access to function keys $\mathsf{sk}_{f_1}, \mathsf{sk}_{f_2}, \ldots$ (and so on) can only learn $f_1(m), f_2(m), \ldots$ (and so on) but nothing more about the message. The system is said to be $q$-bounded collusion resistant if the security holds as long as an adversary gets access to at most $q = q(\lambda)$ function keys. A major drawback of such statically bounded collusion systems is that the collusion bound $q$ must be declared at setup time and is fixed for the entire lifetime of the system. We initiate the study of dynamically bounded collusion resistant functional encryption systems which provide more flexibility in terms of selecting the collusion bound, while reaping the benefits of statically bounded collusion FE systems (such as quantum resistance, simulation security, and general assumptions). Briefly, the virtues of a dynamically bounded scheme can be summarized as: (i) [Fine-grained individualized selection.] It lets each encryptor select the collusion bound by weighing the trade-off between performance overhead and the amount of collusion resilience. (ii) [Evolving encryption strategies.] Since the system is no longer tied to a single collusion bound, thus it allows to dynamically adjust the desired collusion resilience based on any number of evolving factors such as the age of the system, or a number of active users, etc. (iii) [Ease and simplicity of updatability.] None of the system parameters have to be updated when adjusting the collusion bound. That is, the same key $\mathsf{sk}_f$ can be used to decrypt ciphertexts for collusion bound $q = 2$ as well as $q = 2^\lambda$. We construct such a dynamically bounded functional encryption scheme for the class of all polynomial-size circuits under the general assumption of Identity-Based Encryption

Optimal Bounded-Collusion Secure Functional Encryption

We construct private-key and public-key functional encryption schemes secure against adversaries that corrupt an a-priori bounded number of users and obtain their functional keys, from minimal assumptions. For a collusion bound of $Q=Q(\lambda)$ (where $\lambda$ is the security parameter), our public-key (resp. private-key) functional encryption scheme (a) supports the class of all polynomial-size circuits; (b) can be built solely from a vanilla public-key (resp. private-key) encryption scheme; and (c) has ciphertexts that grow linearly with the collusion bound $Q$. Previous constructions were sub-optimal with respect to one or more of the above properties. The first two of these properties are the best possible and any improvement in the third property, namely the ciphertext size dependence on the collusion bound $Q$, can be used to realize an indistinguishability obfuscation scheme. In addition, our schemes are adaptively secure and make black-box use of the underlying cryptographic primitives

Controlled Functional Encryption

3École polytechnique fédérale de Lausanne Motivated by privacy and usability requirements in various sce-narios where existing cryptographic tools (like secure multi-party computation and functional encryption) are not adequate, we in-troduce a new cryptographic tool called Controlled Functional En-cryption (C-FE). As in functional encryption, C-FE allows a user (client) to learn only certain functions of encrypted data, using keys obtained from an authority. However, we allow (and require) the client to send a fresh key request to the authority every time it wants to evaluate a function on a ciphertext. We obtain efficient solu-tions by carefully combining CCA2 secure public-key encryption (or rerandomizable RCCA secure public-key encryption, depend-ing on the nature of security desired) with Yao’s garbled circuit. Our main contributions in this work include developing and for-mally defining the notion of C-FE; designing theoretical and prac-tical constructions of C-FE schemes achieving these definitions for specific and general classes of functions; and evaluating the perfor-mance of our constructions on various application scenarios

Advances in Functional Encryption

Functional encryption is a novel paradigm for public-key encryption that enables both fine-grained access control and selective computation on encrypted data, as is necessary to protect big, complex data in the cloud. In this thesis, I provide a brief introduction to functional encryption, and an overview of my contributions to the area

Reusable garbled circuits and succinct functional encryption

Garbled circuits, introduced by Yao in the mid 80s, allow computing a function f on an input x without leaking anything about f or x besides f(x). Garbled circuits found numerous applications, but every known construction suffers from one limitation: it offers no security if used on multiple inputs x. In this paper, we construct for the first time reusable garbled circuits. The key building block is a new succinct single-key functional encryption scheme. Functional encryption is an ambitious primitive: given an encryption Enc(x) of a value x, and a secret key sk_f for a function f, anyone can compute f(x) without learning any other information about x. We construct, for the first time, a succinct functional encryption scheme for {\em any} polynomial-time function f where succinctness means that the ciphertext size does not grow with the size of the circuit for f, but only with its depth. The security of our construction is based on the intractability of the Learning with Errors (LWE) problem and holds as long as an adversary has access to a single key sk_f (or even an a priori bounded number of keys for different functions). Building on our succinct single-key functional encryption scheme, we show several new applications in addition to reusable garbled circuits, such as a paradigm for general function obfuscation which we call token-based obfuscation, homomorphic encryption for a class of Turing machines where the evaluation runs in input-specific time rather than worst-case time, and a scheme for delegating computation which is publicly verifiable and maintains the privacy of the computation.Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant)United States. Defense Advanced Research Projects Agency (DARPA award FA8750-11-2-0225)United States. Defense Advanced Research Projects Agency (DARPA award N66001-10-2-4089)National Science Foundation (U.S.) (NSF award CNS-1053143)National Science Foundation (U.S.) (NSF award IIS-1065219)Google (Firm

Impossibility Results for Lattice-Based Functional Encryption Schemes

Functional Encryption denotes a form of encryption where a master secret key-holder can control which functions a user can evaluate on encrypted data. Learning With Errors (LWE) (Regev, STOC\u2705) is known to be a useful cryptographic hardness assumption which implies strong primitives such as, for example, fully homomorphic encryption (Brakerski-Vaikuntanathan, FOCS\u2711) and lockable obfuscation (Goyal et al., Wichs et al., FOCS\u2717). Despite its strength, however, there is just a limited number of functional encryption schemes which can be based on LWE. In fact, there are functional encryption schemes which can be achieved by using pairings but for which no secure instantiations from lattice-based assumptions are known: function-hiding inner product encryption (Lin, Baltico et al., CRYPTO\u2717) and compact quadratic functional encryption (Abdalla et al., CRYPTO\u2718). This raises the question whether there are some mathematical barriers which hinder us from realizing function-hiding and compact functional encryption schemes from lattice-based assumptions as LWE. To study this problem, we prove an impossibility result for function-hiding functional encryption schemes which meet some algebraic restrictions at ciphertext encryption and decryption. Those restrictions are met by a lot of attribute-based, identity-based and functional encryption schemes whose security stems from LWE. Therefore, we see our results as important indications why it is hard to construct new functional encryption schemes from LWE and which mathematical restrictions have to be overcome to construct secure lattice-based functional encryption schemes for new functionalities

Secure Computation in Online Social Networks

Apart from their numerous other benefits, online social networks (OSNs) allow users to jointly compute on each other’s data (e.g., profiles, geo-locations, medical records, etc.). Privacy issues naturally arise in this setting due to the sensitive nature of the exchanged information. Ideally, nothing about a user’s data should be revealed to the OSN provider or non-friend users, and even her friends should only learn the output of a joint computation. In this work we propose the first security framework to capture these strong privacy guarantees for general-purpose computation. We also achieve two additional attractive properties: users do not need to be online while their friends compute on their data, and any user value uploaded at the server can be repeatedly used in multiple computations. We formalize our framework in the setting of secure multi-party computation (MPC) and provide two instantiations: the first is a non-trivial adaptation of garbled circuits that converts inputs under different keys to ones under the same key, and the second is based on two-party mixed protocols and involves a novel two-party re-encryption module. We experimentally validate the efficiency of our instantiations using state-of-the-art tools for two concrete use-cases

Robust Non-Interactive Multiparty Computation Against Constant-Size Collusion

Non-Interactive Multiparty Computations (Beimel et al., Crypto 2014) is a very powerful notion equivalent (under some corruption model) to garbled circuits, Private Simultaneous Messages protocols, and obfuscation. We present robust solutions to the problem of Non-Interactive Multiparty Computation in the computational and information-theoretic models. Our results include the first efficient and robust protocols to compute any function in $NC^1$ for constant-size collusions, in the information-theoretic setting and in the computational setting, to compute any function in $P$ for constant-size collusions, assuming the existence of one-way functions. Our constructions start from a Private Simultaneous Messages construction (Feige, Killian Naor, STOC 1994 and Ishai, Kushilevitz, ISTCS 1997) and transform it into a Non-Interactive Multiparty Computation for constant-size collusions. We also present a new Non-Interactive Multiparty Computation protocol for symmetric functions with significantly better communication complexity compared to the only known one of Beimel et al