Optimal Broadcast Encryption from Pairings and LWE

Boneh, Waters and Zhandry (CRYPTO 2014) used multilinear maps to provide a solution to the long-standing problem of public-key broadcast encryption (BE) where all parameters in the system are small. In this work, we improve their result by providing a solution that uses only bilinear maps and Learning With Errors (LWE). Our scheme is fully collusion-resistant against any number of colluders, and can be generalized to an identity-based broadcast system with short parameters. Thus, we reclaim the problem of optimal broadcast encryption from the land of “Obfustopia”. Our main technical contribution is a ciphertext policy attribute based encryption (CP-ABE) scheme which achieves special efficiency properties – its ciphertext size, secret key size, and public key size are all independent of the size of the circuits supported by the scheme. We show that this special CP-ABE scheme implies BE with optimal parameters; but it may also be of independent interest. Our constructions rely on a novel interplay of bilinear maps and LWE, and are proven secure in the generic group model

Tracking Information Flow by Mapping Broadcast Encryption Subgroups to Security Lattices

In this paper we consider scenarios in which a server broadcasts messages with different confidentiality levels to nodes subgroups holding the appropriate clearance. We build on IND-CPA broadcast encryption schemes to preserve the message's confidentiality over a network. Our proposal is that, to verify that information in the server flows to nodes with the appropriate clearances (e.g. verify the use of the correct encryption keys), we can map broadcast subgroups of nodes to levels in information flow security lattices. We implement this idea via a type system and provide a soundness proof with respect to a formally defined secure information flow property for server code

P/polyP/poly Invalidity of the Agr17 Functional Encryption Scheme

Functional encryption (FE) is an advanced topic in the research of cryptography, and the Agr17 FE scheme is one of the major FE schemes. It took the BGG+14 attribute-based encryption (ABE) scheme as a bottom structure, which was upgraded into a `partially hiding predicate encryption\u27 (PHPE) scheme and combined with a fully homomorphic encryption (FHE) scheme. However, there is a remaining problem, the implementation of the modulus reduction, in the Agr17 FE scheme. First, a modulus reduction is necessary for the polynomial-time computability of the scheme. Second, the detailed steps of the modulus reduction were absent in the scheme (including its conference version and full version). Instead, the authors only pointed out several reference works. The author\u27s meaning seemed to be that the modulus reduction of the Agr17 FE scheme can be obtained by directly using or simply generalizing these reference works. Third, these reference works only described various modulus reductions of FHE schemes, without the hint of how to generalize them into the modulus reduction of FE schemes. Finally, any modulus reduction of FHE can not be simply generalized into the modulus reduction of the Agr17 FE scheme due to the following two facts: (1) The Agr17 FE scheme has two moduli, which are the modulus of the FHE ciphertext and of the ABE ciphertext, both are originally superpolynomial in size for processing $P/poly$ functions. (2) Both moduli need to be scaled down to polynomial size, and both of them need to be reduced to the same new modulus, otherwise, the correctness of the scheme will fail. In this paper, we demonstrate that the Agr17 FE scheme is $P/poly$ invalid. More specifically, we show that, when processing $P/poly$ functions, the Agr17 FE scheme cannot be implemented again after its modulus reduction. To show the soundness of our demonstration, we present the statements in two stages. At the first stage, we show that the modulus reduction of the Agr17 FE scheme should be a double modulus reduction, which includes two modulus reductions for the FHE ciphertext and ABE ciphertext, respectively. This double modulus reduction has the following three key points: (1) The modulus reduction for the FHE ciphertext should be seen as a series of Boolean operations, and converted into `attribute quasi-homomorphic operations\u27. (2) The modulus reduction for the ABE ciphertext is a learning-with-errors (LWE) -based modulus reduction, which is an ordinary modulus reduction. (3) The two modulus reductions should obtain the same new modulus, otherwise, the scheme would not be implemented again. At the second stage, we show that the modulus reduction for the ABE ciphertext will destroy the structure of ABE so that the subsequent decryption would not be executed. The reason lies in that the decryption of ABE is an LWE decryption with conditions rather than an ordinary LWE decryption, and the modulus reduction will destroy the conditions of decryption. Besides, to show such invalidity cannot be easily crossed by revising the scheme, we design two revised versions of the Agr17 scheme. The first revised version is a `natural\u27 revised version of the Agr17 scheme. The key point is to change the small modulus inner product into an arithmetic inner product, which can be obtained by the modulus inner product of the ABE ciphertext. The first revised scheme is valid, i.e., the decryption can be implemented correctly. However, the revised scheme is insecure because the decryptor knows much more secret information, and hence the scheme can be broken by collusion attacks with much less cost. The second revised version is an application of the GGH+13b verification circuit technology which transforms a $P/poly$ function into an $NC^1$ circuit. The second revised scheme is valid, but it is far from the design idea of the Agr17 scheme, and its function class is quite limited, that is, those functions which can be equally transformed from $P/poly$ into $NC^1$ by equal verification transformation, rather than any $P/poly$ functions

Optimal Broadcast Encryption and CP-ABE from Evasive Lattice Assumptions

We present a new, simple candidate broadcast encryption scheme for $N$ users with parameter size poly$(\log N)$. We prove security of our scheme under a non-standard variant of the LWE assumption where the distinguisher additionally receives short Gaussian pre-images, while avoiding zeroizing attacks. This yields the first candidate optimal broadcast encryption that is plausibly post-quantum secure, and enjoys a security reduction to a simple assumption. As a secondary contribution, we present a candidate ciphertext-policy attribute-based encryption (CP-ABE) scheme for circuits of a-priori bounded polynomial depth where the parameter size is independent of the circuit size, and prove security under an additional non-standard assumption

Decentralized Multi-Authority ABE for NC^1 from Computational-BDH

Decentralized multi-authority attribute-based encryption (-) is a strengthening of standard ciphertext-policy attribute-based encryption so that there is no trusted central authority: any party can become an authority and there is no requirement for any global coordination other than the creation of an initial set of common reference parameters. Essentially, any party can act as an authority for some attribute by creating a public key of its own and issuing private keys to different users that reflect their attributes. This paper presents the first - proven secure under the standard search variant of bilinear Diffie-Hellman (CBDH) and in the random oracle model. Our scheme supports all access policies captured by 1 circuits. All previous constructions were proven secure in the random oracle model and additionally were based on decision assumptions such as the DLIN assumption, non-standard -type assumptions, or subspace decision assumptions over composite-order bilinear groups

Distributed Broadcast Encryption from Bilinear Groups

In this work, we show that obfuscation is not necessary for DBE, and we present two DBE schemes from standard assumptions in prime-order bilinear groups. Our constructions are conceptually simple, satisfy the strong notion of adaptive security, and are concretely efficient. In fact, their performance, in terms of number of group elements and efficiency of the algorithms, is comparable with that of traditional (non distributed) broadcast encryption schemes from bilinear groups. Distributed broadcast encryption (DBE) improves on the traditional notion of broadcast encryption by eliminating the key-escrow problem: In a DBE system, users generate their own secret keys non-interactively without the help of a trusted party. Then anyone can broadcast a message for a subset $S$ of the users, in such a way that the resulting ciphertext size is sublinear in (and, ideally, independent of) $|S|$. Unfortunately, the only known constructions of DBE requires heavy cryptographic machinery, such as general-purpose indistinguishability obfuscation, or come without a security proof. In this work, we place DBE on similar footing as traditional (non-distributed) broadcast encryption: We present two practical DBE schemes from standard assumptions in prime-order bilinear groups. Our constructions are conceptually simple, satisfy the strong notion of adaptive security, and are concretely efficient. Their performance, in terms of number of group elements and efficiency of the algorithms, is comparable with that of traditional broadcast encryption schemes from bilinear groups

On the Price of Concurrency in Group Ratcheting Protocols

Post-Compromise Security, or PCS, refers to the ability of a given protocol to recover—by means of normal protocol operations—from the exposure of local states of its (otherwise honest) participants. While PCS in the two-party setting has attracted a lot of attention recently, the problem of achieving PCS in the group setting—called group ratcheting here—is much less understood. On the one hand, one can achieve excellent security by simply executing, in parallel, a two-party ratcheting protocol (e.g., Signal) for each pair of members in a group. However, this incurs $\mathcal{O}(n)$ communication overhead for every message sent, where $n$ is the group size. On the other hand, several related protocols were recently developed in the context of the IETF Messaging Layer Security (MLS) effort that improve the communication overhead per message to $\mathcal{O}(\log n)$. However, this reduction of communication overhead involves a great restriction: group members are not allowed to send and recover from exposures concurrently such that reaching PCS is delayed up to $n$ communication time slots (potentially even more). In this work we formally study the trade-off between PCS, concurrency, and communication overhead in the context of group ratcheting. Since our main result is a lower bound, we define the cleanest and most restrictive setting where the tension already occurs: static groups equipped with a synchronous (and authenticated) broadcast channel, where up to $t$ arbitrary parties can concurrently send messages in any given round. Already in this setting, we show in a symbolic execution model that PCS requires $\Omega(t)$ communication overhead per message. Our symbolic model permits as building blocks black-box use of (even dual ) PRFs, (even key-updatable) PKE (which in our symbolic definition is at least as strong as HIBE), and broadcast encryption, covering all tools used in previous constructions, but prohibiting the use of exotic primitives. To complement our result, we also prove an almost matching upper bound of $\mathcal{O}(t\cdot(1+\log(n/t)))$, which smoothly increases from $\mathcal{O}(\log n)$ with no concurrency, to $\mathcal{O}(n)$ with unbounded concurrency, matching the previously known protocols

Registered (Inner-Product) Functional Encryption

Registered encryption (Garg et al., TCC\u2718) is an emerging paradigm that tackles the key-escrow problem associated with identity-based encryption by replacing the private-key generator with a much weaker entity known as the key curator. The key curator holds no secret information, and is responsible to: (i) update the master public key whenever a new user registers its own public key to the system; (ii) provide helper decryption keys to the users already registered in the system, in order to still enable them to decrypt after new users join the system. For practical purposes, tasks (i) and (ii) need to be efficient, in the sense that the size of the public parameters, of the master public key, and of the helper decryption keys, as well as the running times for key generation and user registration, and the number of updates, must be small. In this paper, we generalize the notion of registered encryption to the setting of functional encryption (FE). As our main contribution, we show an efficient construction of registered FE for the special case of ({\it attribute hiding}) inner-product predicates, built over asymmetric bilinear groups of prime order. Our scheme supports a {\it large} attribute universe and is proven secure in the bilinear generic group model. We also implement our scheme and experimentally demonstrate the efficiency requirements of the registered settings. Our second contribution is a feasibility result where we build registered FE for P/poly based on indistinguishability obfuscation and somewhere statistically binding hash functions

How to Use (Plain) Witness Encryption: Registered ABE, Flexible Broadcast, and More

Witness encryption is a generalization of public-key encryption where the public key can be any NP statement x and the associated decryption key is any witness w for x. While early constructions of witness encryption relied on multilinear maps and indistinguishability obfuscation (iO), recent works have provided direct constructions of witness encryption that are more efficient than iO (and also seem unlikely to yield iO). Motivated by this progress, we revisit the possibility of using witness encryption to realize advanced cryptographic primitives previously known only in obfustopia. In this work, we give new constructions of trustless encryption systems from plain witness encryption (in conjunction with the learning-with-errors assumption): (1) flexible broadcast encryption (a broadcast encryption scheme where users choose their own secret keys and users can encrypt to an arbitrary set of public keys); and (2) registered attribute-based encryption (a system where users choose their own keys and then register their public key together with a set of attributes with a deterministic and transparent key curator). Both primitives were previously only known from iO. We also show how to use our techniques to obtain an optimal broadcast encryption scheme in the random oracle model. Underlying our constructions is a novel technique for using witness encryption based on a new primitive which we call function-binding hash functions. Whereas a somewhere statistically binding hash function statistically binds a digest to a few bits of the input, a function-binding hash function statistically binds a digest to the output of a function of the inputs. As we demonstrate in this work, function-binding hash functions provide us new ways to leverage the power of plain witness encryption and use it as the foundation of advanced cryptographic primitives. Finally, we show how to build function-binding hash functions for the class of disjunctions of block functions from leveled homomorphic encryption; this in combination with witness encryption yields our main results

Multi-Party Functional Encryption

We initiate the study of multi-party functional encryption (MPFE) which unifies and abstracts out various notions of functional encryption which support distributed ciphertexts or secret keys, such as multi-input FE, multi-client FE, decentralized multi-client FE, multi-authority FE, dynamic decentralized FE, adhoc multi-input FE and such others. Using our framework, we identify several gaps in the literature and provide some constructions to fill these: 1) Multi-Authority ABE with Inner Product Computation: The recent work of Abdalla et al. (ASIACRYPT\u2720) constructed a novel ``composition\u27\u27 of Attribute Based Encryption (ABE) and Inner Product Functional Encryption (IPFE), namely functional encryption schemes that combine the access control functionality of attribute based encryption with the possibility of performing linear operations on the encrypted data. In this work, we extend the access control component to support the much more challenging multi-authority setting, i.e. ``lift\u27\u27 the primitive of ABE in their construction to multi-authority ABE for the same class of access control policies (LSSS structures). This yields the first construction of a nontrivial multi-authority FE beyond ABE from simple assumptions on pairings to the best of our knowledge. Our techniques can also be used to generalize the decentralized attribute based encryption scheme of Michalevsky and Joye (ESORICS\u2718) to support inner product computation on the message. While this scheme only supports inner product predicates which is less general than those supported by the Lewko-Waters (EUROCRYPT\u2711) construction, it supports policy hiding which the latter does not. Our extension inherits these features and is secure based on the $k$-linear assumption, in the random oracle model. 2. Function Hiding DDFE: The novel primitive of dynamic decentralized functional encryption (DDFE) was recently introduced by Chotard et al. (CRYPTO\u2720), where they also provided the first construction for inner products. However, the primitive of DDFE does not support function hiding, which is a significant limitation for several applications. In this work, we provide a new construction for inner product DDFE which supports function hiding. To achieve our final result, we define and construct the first function hiding multi-client functional encryption (MCFE) scheme for inner products, which may be of independent interest. 3. Distributed Ciphertext-Policy ABE: We provide a distributed variant of the recent ciphertext-policy attribute based encryption scheme, constructed by Agrawal and Yamada (EUROCRYPT\u2720). Our construction supports $NC^1$ access policies, and is secure based on ``Learning With Errors\u27\u27 and relies on the generic bilinear group model as well as the random oracle model. Our new MPFE abstraction predicts meaningful new variants of functional encryption as useful targets for future work