Functional encryption is an emerging paradigm for public-key encryption that enables finegrained control of access to encrypted data. In this work, we present new perspectives on security definitions for functional encryption, as well as new lower bounds on what can be achieved. Our main contributions are as follows: • We show a lower bound for functional encryption that satisfies a weak (non-adaptive) simulation-based security notion, via pseudo-random functions. This is the first lower bound that exploits unbounded collusions in an essential way. • We put forth and discuss a simulation-based notion of security for functional encryption, with an unbounded simulator (called USIM). We show that this notion interpolates indistinguishability and simulation-based security notions, and has strong correlations to results and barriers in the zero-knowledge and multi-party computation literature.
Functional encryption is an emerging paradigm for public-key encryption that enables finegrained control of access to encrypted data. In this work, we present new perspectives on security definitions for functional encryption, as well as new lower bounds on what can be achieved. Our main contributions are as follows: • We show a lower bound for functional encryption that satisfies a weak (non-adaptive) simulation-based security notion, via pseudo-random functions. This is the first lower bound that exploits unbounded collusions in an essential way. • We put forth and discuss a simulation-based notion of security for functional encryption, with an unbounded simulator (called USIM). We show that this notion interpolates indistinguishability and simulation-based security notions, and has strong correlations to results and barriers in the zero-knowledge and multi-party computation literature.
Functional encryption provides fine-grained access control for encrypted data, allowing each user to learn only specific functions of the encrypted data. We study the notion of hierarchical functional encryption, which augments functional encryption with delegation capabilities, offering significantly more expressive access control. We present a generic transformation that converts any general-purpose public-key functional encryption scheme into a hierarchical one without relying on any additional assumptions. This significantly refines our understanding of the power of functional encryption, showing that the existence of functional encryption is equivalent to that of its hierarchical generalization. Instantiating our transformation with the existing functional encryption schemes yields a variety of hierarchical schemes offering various trade-offs between their delegation capabilities (i.e., the depth and width of their hierarchical structures) and underlying assumptions. When starting with a scheme secure against an unbounded number of collusions, we can support arbitrary hierarchical structures. In addition, even when starting with schemes that are secure against a bounded number of collusions (which are known to exist under rather minimal assumptions such as the existence of public-key encryption and shallow pseudorandom generators), we can support hierarchical structures of bounded depth and width.
Functional encryption (FE) is a versatile paradigm that enables fine-grained access control over encrypted data. Despite its potential, achieving the gold standard of simulation-based security for FE is impossible in full generality. Known impossibility results demonstrate that simulation security cannot be attained if an adversary in the security experiment is permitted either an unbounded number of functional key queries or an unbounded number of challenge ciphertexts. In this work, we circumvent these fundamental barriers by considering two distinct memory-restricted settings: the Bounded Quantum Storage Model and the Bounded Classical Storage Model. In these settings, the plain model impossibility results no longer apply, allowing us to obtain new positive results. Specifically, we construct two adaptively simulation-secure FE schemes in the Bounded Quantum Storage Model: 1) Many functional key scheme: A construction supporting many functional key queries and a single challenge ciphertext, assuming only the existence of one-way functions. 2) Many ciphertext scheme: An information-theoretic secure construction supporting a single non-adaptive functional key, many challenge ciphertexts, and many adaptive functional key queries. Furthermore, we demonstrate that both schemes can be ported to the Bounded Classical Storage Model, assuming the existence of disappearing grey-box obfuscation.
Functional encryption is a powerful cryptographic primitive that enables fine-grained access to encrypted data and underlies numerous applications. Although the ideal security notion for FE, simulation security, has been shown to be impossible in the plain classical setting, those impossibility results rely on inherently classical arguments. This raises a fundamental question: can simulation-secure FE be realized in the quantum regime or in alternative models?
We resolve both directions of this question. On the negative side, we show that the classical impossibility results largely extend to the quantum setting. When the adversary can submit an unbounded number of challenge messages, we establish an unconditional impossibility, matching the classical barrier. In the case where the adversary may obtain many functional keys, classical arguments only yield impossibility under the assumption of pseudorandom functions; we strengthen this by proving impossibility under the potentially weaker assumption of pseudorandom quantum states. We additionally give an independent impossibility based solely on public-key encryption with classical public-keys. Since public-key encryption is not known to imply pseudorandom states, this yields complementary evidence of the barrier and, in particular, establishes unconditional impossibility of public-key functional encryption with classical public-keys. A key technical ingredient in our proofs is a novel incompressibility property for pseudorandom states, which may be of independent interest.
On the positive side, we show how to circumvent these fundamental barriers in memory-restricted models, where the adversary's quantum or classical memory is bounded. In this setting, we obtain new feasibility results for simulation-secure FE that allow many challenge ciphertexts or many functional key queries.
We provide a formalization of the emergent notion of “functional encryption,” as well as introduce various security notions for it, and study relations among the latter. In particular, we show that indistinguishability and semantic security based notions of security are inequivalent for functional encryption in general; in fact, “adaptive” indistinguishability does not even imply “non-adaptive” semantic security. This is alarming given the large body of work employing (special cases of) the former. We go on to show, however, that in the “non-adaptive” case an equivalence does hold between indistinguishability and semantic security for what we call preimage sampleable schemes. We take this as evidence that for preimage sampleable schemes an indistinguishability based notion may be acceptable in practice. We show that some common functionalities considered in the literature satisfy this requirement.
Abstract. This work attempts to clarify to what extent simulationbased security (SIM-security) is achievable for functional encryption (FE) and its relation to the weaker indistinguishability-based security (INDsecurity). Our main result is a compiler that transforms any FE scheme for the general circuit functionality (which we denote by Circuit-FE) meeting indistinguishability-based security (IND-security) to a Circuit-FE scheme meeting SIM-security, where: – In the random oracle model, the resulting scheme is secure for an unbounded number of encryption and key queries, which is the strongest security level one can ask for. – In the standard model, the resulting scheme is secure for a bounded number of encryption and non-adaptive key queries, but an unbounded number of adaptive key queries. This matches known impossibility results and improves upon Gorbunov et al. [CRYPTO’12] (which is only secure for non-adaptive key queries).
Abstract. The notion of multi-input functional encryption (MI-FE) was recently introduced by Goldwasser et al. [EUROCRYPT’14] as a means to non-interactively compute aggregate information on the joint private data of multiple users. A fundamental limitation of their work, however, is that the total number of users (which corresponds to the arity of the functions supported by the MI-FE scheme) must be a priori bounded and fixed at the system setup time. In this work, we overcome this limitation by introducing the notion of unbounded input MI-FE that supports the computation of functions with unbounded arity. We construct such an MI-FE scheme with indis-tinguishability security in the selective model based on the existence of public-coin differing-inputs obfuscation for turing machines and collision-resistant hash functions. Our result enables several new exciting applications, including a new paradigm of on-the-fly secure multiparty computation where new users can join the system dynamically.