Functional Encryption (FE) expands traditional public-key encryption in two different ways: it supports fine-grained access control and allows learning a function of the encrypted data. In this paper, we review all FE classes, describing their functionalities and main characteristics. In particular, we mention several schemes for each class, providing their security assumptions and comparing their properties. To our knowledge, this is the first survey that encompasses the entire FE family.
Functional Encryption (FE) expands traditional public-key encryption in two different ways: it supports fine-grained access control and allows learning a function of the encrypted data. In this paper, we review all FE classes, describing their functionalities and main characteristics. In particular, we mention several schemes for each class, providing their security assumptions and comparing their properties. To our knowledge, this is the first survey that encompasses the entire FE family.
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 powerful primitive enabling fine-grained access to encrypted data. In an FE scheme, secret keys (“tokens”) correspond to functions; a user in possession of a ciphertext ct = Enc(x) and a token TKf for the function f can compute f(x) but learn nothing else about x. An active area of research over the past few years has focused on the development of ever more expressive FE schemes. In this work we introduce the notion of multi-input functional encryption. Here, informally, a user in possession of a token TKf for an n-ary function f and multiple ciphertexts ct1 = Enc(x1), . . . , ctn = Enc(xn) can compute f(x1, . . . , xn) but nothing else about the {xi}. Besides introducing the notion, we explore the feasibility of multi-input FE in the public-key and symmetric-key settings, with respect to both indistinguishability-based and simulation-based definitions of security. ∗ACS. Email: sgordon@appcomsci.com. †Department of Computer Science, University of Maryland. Email: jkatz@cs.umd.edu. This research was sponsored by NSF award #1223623 and by the US Army Research Laboratory and the UK Ministry of Defence under Agreement Number W911NF-06-3-0001. ‡Department of Computer Science, University of Maryland. Email: fenghao@cs.umd.edu. §Department of Computer Science, University of Maryland. Email: elaine@cs.umd.edu. This work is partially supported by NSF award CNS-1314857 and a Google Research Award. ¶Department of Computer Science, Virginia Commonwealth University. Email: hszhou@vcu.edu. This work is partially supported by an NSF CI postdoctoral fellowship, and was mostly done while at the University of Maryland.
In recent years, there has been great interest in Functional Encryption (FE), a generaliza-tion of traditional encryption where a token enables a user to learn a specific function of the encrypted data and nothing else. In this paper we put forward a new generalization of FE that we call M ergeable FE (mFE). In a mFE system, given a ciphertext c1 encrypting m1 and a ciphertext c2 encrypting m2, it is possible to produce in an oblivious way (i.e., given only the public-key and without knowledge of the messages, master secret-key or any other aux-iliary information) a ciphertext encrypting the string m1||m2 under the security constraint that this new ciphertext does not leak more information about the original messages than what may be leaked from the new ciphertext using the tokens. For instance, suppose that the adversary is given the token for the function f(·) defined so that for strings x ∈ {0, 1}n, f(x) 4 = g(x) for some function g: {0, 1}n → {0, 1} and for strings y = (x1||x2) ∈ {0, 1}2n, f(x1||x2) 4 = g(x1) ∨ g(x2). Furthermore, suppose that the adversary gets a ciphertext c
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 (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.
Functional encryption provides a general access control over the encrypted data, where only the receiver with attribute that satisfies control policy function of policy parameter (i.e. ) can decrypt its ciphertext. Special cases of functional encryption include (anonymous-) (hierarchical) identity-based encryption, fuzzy identity-based encryption, attribute-based encryption, public key encryption with keyword search, spatial encryption, inner-product encryption, hidden-vector encryption and predicate encryption. In general functional encryption systems, the control policy function can be set flexibly. The main gap among these functional encryption schemes lies in the policy functions that associates with the secret keys. In this work, we first investigate several functional encryption schemes, and then formalize and unify the functionality description of the control policies for these schemes. After giving a general definition and security model, we present the relationship and transformations among functional encryption schemes when the equivalence of these different policy functions is employed.