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. 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).
One of the main lines of research in functional encryption (FE) has consisted in studying the security notions for FE and their achievability. This study was initiated by [Boneh et al. { TCC’11, O’Neill { ePrint’10] where it was rst shown that for FE the indistinguishabilitybased (IND) security notion is not sucient in the sense that there are FE schemes that are provably IND-Secure but concretely insecure. For this reason, researchers investigated the achievability of Simulation-based (SIM) security, a stronger notion of security. Unfortunately, the above-mentioned works and others [e.g., Agrawal et al. { CRYPTO’13] have shown strong impossibility results for SIM-Security. One way to overcome these impossibility results was rst
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.
Functional encryption (FE) has more fine-grained control to encrypted data than traditional encryption schemes. The well-accepted security of FE is indistinguishability-based security (IND-FE) and simulation-based security (SIMFE), but the security is not sufficient.For example, if an adversary has the ability to access a vector of ciphertexts and can ask to open some information of the messages, such as coins used in the encryption or secret key in multikey setting, whether the privacy of the unopened messages is guaranteed.This is called selective opening attack (SOA).In this paper, we propose a stronger security of FE which is secure against SOA (we call SO-FE) and propose a concrete construction of SO-FE scheme in the standard model.Our scheme is a non-adaptive IND-FE which satisfies selective opening secure in the simulation sense.In addition, the scheme can encrypt messages of any bit length other than bitwise and it is secure against SOA-C and SOAK simultaneously while the two attacks were appeared in different model before.According to the different functionality f, our scheme can specialize as IBE, ABE and even PE schemes secure against SOA.
This work furthers the exploration of meaningful definitions for security of Functional Encryption. We propose new simulation based definitions for function privacy in addition to data privacy and study their achievability. In addition, we improve efficiency/ underlying assumptions/ security achieved by existing inner product Functional Encryption and Property Preserving Encryption schemes, in both the private and public key setting. Our results can be summarized as follows: • We present a new simulation based definition, which we call Relax-AD-SIM, that lies between simulation based (SIM) and indistinguishability based (IND) definitions for data privacy, and implies the function privacy definition of [BRS13a]. Our definition relaxes the requirements on the simulator to bypass impossibility of SIM in the standard model. We show that the inner product FE scheme of [KSW08] enjoys Relax-AD-SIM security for function hiding and the inner product FE scheme of [LOS10] enjoys Relax-AD-SIM security for data hiding. • We study whether known impossibilities for achieving strong SIM based security imply actual real world attacks. For this, we present a new UC-style SIM based definition of security that captures both data and function hiding, both public key and symmetric key settings and represents the “dream” security of FE. While known impossibilities rule out its achievability in the standard model, we show, surprisingly, that it can be achieved in the generic group model for Inner Product FE ([KSW08]). This provides evidence that FE implementations may enjoy extremely strong security against a large class of real world attacks, namely generic attacks. It also implies a program obfuscator for the inner product functionality in the generic group model, which is related to the hyperplane-membership obfuscator of [CRV10]. • We provide several improvements to known constructions of Inner Product FE. In the private key setting, the construction by Shen et al. was based on non-standard assumptions, used composite order groups, and only achieved selective security. We give the first construction of a symmetric key inner product FE which is built using prime order groups, and is fully secure under the standard DLIN assumption. Our scheme is more efficient in the size of key and ciphertext than [SSW09], when the latter is converted to prime-order groups. We also port the public key inner product scheme of [KSW08] to prime order groups. • We give the first standard model construction of a property preserving encryption (PPE) scheme [PR12] for inner-products. Our scheme is secure under the DLIN assumption and satisfies the strongest definition of security – Left-or-Right security. Note that previously known constructions were only known to be secure in the generic group model. ∗UIUC. Email: sagrawl2@illinois.edu. †I.I.T, Delhi. Email: shweta.a@gmail.com. ‡UIUC. Email: bsaikrishna7393@gmail.com. §UCLA Email: abishekk@cs.ucla.edu. ¶UIUC. Email: manojmp@gmail.com. ‖UCLA Email: sahai@cs.ucla.edu.
Abstract Functional encryption (FE) can provide a fine-grained access control on the encrypted message. Therefore, it has been applied widely in security business. The previous works about functional encryptions most focused on the deterministic functions. The randomized algorithm has wide application, such as securely encryption algorithms against chosen ciphertext attack, privacy-aware auditing. Based on this, FE for randomized functions was proposed. The existing constructions are provided in a weaker selective security model, where the adversary is forced to output the challenge message before the start of experiment. This security is not enough in some scenes. In this work, we present a novel construction for FE, which supports the randomized functionalities. We use the technology of key encapsulated mechanism to achieve adaptive security under the simulated environment, where the adversary is allowed to adaptively choose the challenge message at any point in time. Our construction is built based on indistinguishability obfuscation, non-interactive witness indistinguishable proofs and perfectly binding commitment scheme.