Multi-Client Inner-Product Functional Encryption in the Random-Oracle Model

International audienceMulti-client functional encryption (MCFE) is an extension of functional encryption (FE) in which the decryption procedure involves ciphertexts from multiple parties. It is particularly useful in the context of data outsourcing and cloud computing where the data may come from different sources and where some data centers or servers may need to perform different types of computation on this data. In order to protect the privacy of the encrypted data, the server, in possession of a functional decryption key, should only be able to compute the final result in the clear, but no other information regarding the encrypted data. In this paper, we consider MCFE schemes supporting encryption labels, which allow the encryptor to limit the amount of possible mix-and-match that can take place during the decryption. This is achieved by only allowing the decryption of ciphertexts that were generated with respect to the same label. This flexible form of FE was already investigated by Chotard et al. at Asiacrypt 2018 and Abdalla et al. at Asiacrypt 2019. The former provided a general construction based on different standard assumptions, but its ciphertext size grows quadratically with the number of clients. The latter gave a MCFE based on Decisional Diffie-Hellman (DDH) assumption which requires a small inner-product space. In this work, we overcome the deficiency of these works by presenting three constructions with linear-sized ciphertexts based on the Matrix-DDH (MDDH), Decisional Composite Residuosity (DCR) and Learning with Errors (LWE) assumption in the random-oracle model. We also implement our constructions to evaluate their concrete efficiency

Verifiable Functional Encryption using Intel SGX

Most functional encryption schemes implicitly assume that inputs to decryption algorithms, i.e., secret keys and ciphertexts, are generated honestly. However, they may be tampered by malicious adversaries. Thus, verifiable functional encryption (VFE) was proposed by Badrinarayanan et al. in ASIACRYPT 2016 where anyone can publicly check the validity of secret keys and ciphertexts. They employed indistinguishability-based (IND-based) security due to an impossibility result of simulation-based (SIM-based) VFE even though SIM-based security is more desirable. In this paper, we propose a SIM-based VFE scheme. To bypass the impossibility result, we introduce a trusted setup assumption. Although it appears to be a strong assumption, we demonstrate that it is reasonable in a hardware-based construction, e.g., Fisch et al. in ACM CCS 2017. Our construction is based on a verifiable public-key encryption scheme (Nieto et al. in SCN 2012), a signature scheme, and a secure hardware scheme, which we refer to as VFE-HW. Finally, we discuss an our implementation of VFE-HW using Intel Software Guard Extensions (Intel SGX)

Private Stream Aggregation from Labeled Secret Sharing Schemes

The concept of private stream aggregation (PSA) has been proposed by Shi et al. (NDSS 2011) to allow for data analysis in a privacy-preserving manner. In this work, we introduce the notion of labeled secret sharing (LaSS) schemes and show how to use it to construct PSA schemes. We also show how to realize LaSS using pseudorandom functions or alternatively with a hash function modeled as a random oracle and how it can be used to construct PSA schemes. Additionally, we revisit the security model of Becker et al. (NDSS 2018) and describe stronger security notions for PSA. We then present additional constructions achieving the stronger security notions by relying on recent results on multi-client functional encryption. For all of our constructions, we present implementations to show their practicality and the performance gains over existing solutions

Multi-Client Functional Encryption for Separable Functions

In this work, we provide a compiler that transforms a single-input functional encryption scheme for the class of polynomially bounded circuits into a multi-client functional encryption (MCFE) scheme for the class of separable functions. An n-input function f is called separable if it can be described as a list of polynomially bounded circuits f^1, ... , f^n s.t. f(x_1, ... , x_n)= f^1(x_1)+ ... + f^n(x_n) for all x_1 ,... , x_n. Our compiler extends the works of Brakerski et al. [Eurocrypt 2016] and of Komargodski et al. [Eurocrypt 2017] in which a generic compiler is proposed to obtain multi-input functional encryption (MIFE) from single-input functional encryption. Our construction achieves the stronger notion of MCFE but for the less generic class of separable functions. Prior to our work, a long line of results has been proposed in the setting of MCFE for the inner-product functionality, which is a special case of a separable function. We also propose a modified version of the notion of decentralized MCFE introduced by Chotard et al. [Asiacrypt 2018] that we call outsourceable mulit-client functional encryption (OMCFE). Intuitively, the notion of OMCFE makes it possible to distribute the load of the decryption procedure among at most n different entities, which will return decryption shares that can be combined (e.g., additively) thus obtaining the output of the computation. This notion is especially useful in the case of a very resource consuming decryption procedure, while the combine algorithm is non-time consuming. We also show how to extend the presented MCFE protocol to obtain an OMCFE scheme for the same functionality class

2-Step Multi-Client Quadratic Functional Encryption from Decentralized Function-Hiding Inner-Product

In this paper, we present a multi-client quadratic functional encryption (MCQFE) scheme from function-hiding inner-product (FHIP). The main challenge in such construction is that all the clients require the access to the master secret key of the underlying FHIP scheme, which clearly breaches the security. To overcome this challenge, we present an efficient decentralized version of FHIP scheme of Lin (Crypto 16). This leads to a 2-step MCQFE (2-MCQFE) scheme. In a 2-step MCQFE scheme, the encryption phase is a (non-interactive) protocol among clients and a set of honest-but-curious authorities. More precisely, clients are the owner of messages and the master secret-key of the underlying FHIP is shared among authorities. In the first step, the client publishes a pre-ciphertext ``pct\u27\u27 associated with its message. Then in the second step, each authority generates its share ``ct_i\u27\u27 extracted from the pre-ciphertext. The public aggregation of these shares ``ct_i\u27\u27 will generate the target ciphertext ``ct\u27\u27 which then would be applied on the functional key ``sk_F\u27\u27 to compute the quadratic functionality. The security model is strong enough to consider no trust among clients and authorities, and also the revelation of some secret keys (of clients or authorities) through corruptions. We instantiate our 2-MCQFE scheme and prove its security in the random-oracle model based on the SXDH assumption. Moreover, we show that its security holds as long as at least one of the authorities is not corrupted

(Inner-Product) Functional Encryption with Updatable Ciphertexts

We propose a novel variant of functional encryption which supports ciphertext updates, dubbed ciphertext-updatable functional encryption (CUFE). Such a feature further broadens the practical applicability of the functional-encryption paradigm and allows for fine-grained access control even after a ciphertext is generated. Updating ciphertexts is carried out via so-called update tokens which a dedicated party can use to convert ciphertexts. However, allowing update tokens requires some care for the security definition. Our contribution is three-fold: a) We define our new primitive with a security notion in the indistinguishability setting. Within CUFE, functional decryption keys and ciphertexts are labeled with tags such that only if the tags of the decryption key and the ciphertext match, then decryption succeeds. Furthermore, we allow ciphertexts to switch their tags to any other tag via update tokens. Such tokens are generated by the holder of the main secret key and can only be used in the desired direction. b) We present a generic construction of CUFE for any functionality as well as predicates different from equality testing on tags which relies on the existence of indistinguishability obfuscation (iO). c) We present a practical construction of CUFE for the inner-product functionality from standard assumptions (i.e., LWE) in the random-oracle model. On the technical level, we build on the recent functional-encryption schemes with fine-grained access control and linear operations on encrypted data (Abdalla et al., AC\u2720) and introduce an additional ciphertext-updatability feature. Proving security for such a construction turned out to be non-trivial, particularly when revealing keys for the updated challenge ciphertext is allowed. Overall, such construction enriches the set of known inner-product functional-encryption schemes with the additional updatability feature of ciphertexts

Compact FE for Unbounded Attribute-Weighted Sums for Logspace from SXDH

This paper presents the first functional encryption (FE) scheme for the attribute-weighted sum (AWS) functionality that supports the uniform model of computation. In such an FE scheme, encryption takes as input a pair of attributes (x,z) where the attribute x is public while the attribute z is private. A secret key corresponds to some weight function f, and decryption recovers the weighted sum f(x)z. This is an important functionality with a wide range of potential real life applications, many of which require the attribute lengths to be flexible rather than being fixed at system setup. In the proposed scheme, the public attributes are considered as binary strings while the private attributes are considered as vectors over some finite field, both having arbitrary polynomial lengths that are not fixed at system setup. The weight functions are modeled as Logspace Turing machines. Prior schemes [Abdalla, Gong, and Wee, CRYPTO 2020 and Datta and Pal, ASIACRYPT 2021] could only support non-uniform Logspace. The proposed scheme is built in asymmetric prime-order bilinear groups and is proven adaptively simulation secure under the well-studied symmetric external Diffie-Hellman (SXDH) assumption against an arbitrary polynomial number of secret key queries both before and after the challenge ciphertext. This is the best possible level of security for FE as noted in the literature. As a special case of the proposed FE scheme, we also obtain the first adaptively simulation secure inner-product FE (IPFE) for vectors of arbitrary length that is not fixed at system setup. On the technical side, our contributions lie in extending the techniques of Lin and Luo [EUROCRYPT 2020] devised for payload hiding attribute-based encryption (ABE) for uniform Logspace access policies avoiding the so-called “one-use” restriction in the indistinguishability-based security model as well as the “three-slot reduction” technique for simulation-secure attribute-hiding FE for non-uniform Logspace devised by Datta and Pal [ASIACRYPT 2021] to the context of simulation-secure attribute-hiding FE for uniform Logspace

Non-Interactive Anonymous Router

Anonymous routing is one of the most fundamental online privacy problems and has been studied extensively for decades. Almost all known approaches for anonymous routing (e.g., mix-nets, DC-nets, and others) rely on multiple servers or routers to engage in some {\it interactive} protocol; and anonymity is guaranteed in the {\it threshold} model, i.e., if one or more of the servers/routers behave honestly. Departing from all prior approaches, we propose a novel {\it non-interactive} abstraction called a Non-Interactive Anonymous Router (NIAR), which works even with a {\it single untrusted router}. In a NIAR scheme, suppose that $n$ senders each want to talk to a distinct receiver. A one-time trusted setup is performed such that each sender obtains a sending key, each receiver obtains a receiving key, and the router receives a {\it token} that ``encrypts\u27\u27 the permutation mapping the senders to receivers. In every time step, each sender can encrypt its message using its sender key, and the router can use its token to convert the $n$ ciphertexts received from the senders to $n$ {\it transformed ciphertexts}. Each transformed ciphertext is delivered to the corresponding receiver, and the receiver can decrypt the message using its receiver key. Imprecisely speaking, security requires that the untrusted router, even when colluding with a subset of corrupt senders and/or receivers, should not be able to compromise the privacy of honest parties, including who is talking to who, and the message contents. We show how to construct a communication-efficient NIAR scheme with provable security guarantees based on the standard Decisional Linear assumption in suitable bilinear groups. We show that a compelling application of NIAR is to realize a Non-Interactive Anonymous Shuffler (NIAS), where an untrusted server or data analyst can only decrypt a permuted version of the messages coming from $n$ senders where the permutation is hidden. NIAS can be adopted to construct privacy-preserving surveys, differentially private protocols in the shuffle model, and pseudonymous bulletin boards. Besides this main result, we also describe a variant that achieves fault tolerance when a subset of the senders may crash. Finally, we further explore a paranoid notion of security called full insider protection, and show that if we additionally assume sub-exponentially secure Indistinguishability Obfuscation and as sub-exponentially secure one-way functions, one can construct a NIAR scheme with paranoid security