Verifiable Computation Research Articles

Privacy-preserving verifiable delegation of polynomial and matrix functions

AbstractOutsourcing computation has gained significant popularity in recent years due to the development of cloud computing and mobile services. In a basic outsourcing model, a client delegates computation of a function f on an input x to a server. There are two main security requirements in this setting: guaranteeing the server performs the computation correctly, and protecting the client’s input (and hence the function value) from the server. The verifiable computation model of Gennaro, Gentry and Parno achieves the above requirements, but the resulting schemes lack efficiency. This is due to the use of computationally expensive primitives such as fully homomorphic encryption (FHE) and garbled circuits, and the need to represent f as a Boolean circuit. Also, the security model does not allow verification queries, which implies the server cannot learn if the client accepts the computation result. This is a weak security model that does not match many real life scenarios. In this paper, we construct efficient (i.e., without using FHE, garbled circuits and Boolean circuit representations) verifiable computation schemes that provide privacy for the client’s input, and prove their security in a strong model that allows verification queries. We first propose a transformation that provides input privacy for a number of existing schemes for verifiable delegation of multivariate polynomial f over a finite field. Our transformation is based on noisy encoding of x and keeps x semantically secure under the noisy curve reconstruction (CR) assumption. We then propose a construction for verifiable delegation of matrix-vector multiplication, where the delegated function f is a matrix and the input to the function is a vector. The scheme uses PRFs with amortized closed-form efficiency and achieves high efficiency. We outline applications of our results to outsourced two-party protocols.

Secure multiparty learning from the aggregation of locally trained models

In many applications, multiple parties would benefit from a precise learning model trained from the aggregated dataset. However, the trivial method that all the data is aggregated into one datacenter and processed centrally is not appropriate when data privacy is a significant concern. In this paper, we propose a new framework for secure multi-party learning and construct a concrete scheme by incorporating aggregate signature and proxy re-encryption techniques. Unlike the previous solutions for multi-party privacy-preserving machine learning, we don't use encryption algorithm to encrypt the whole dataset or the intermediate values during the training process. In our scheme, secure verifiable computation delegation is utilized to privately label a public dataset from the aggregation of locally trained models. Using these newly generated labeled data items, the participants can update their learning models with great accuracy improvement. Further, we prove that the proposed scheme satisfies the desired security properties, and the experimental analysis on MNIST and HAM10000 shows that it is highly efficient.

Verifiable inner product computation on outsourced database for authenticated multi-user data sharing

With the rapid development of cloud computing, the practical applications such as the machine learning based on the outsourced data have been investigated in the data sharing setting. In machine learning, the inner product is a necessary primitive to analyze the description statistics. However, the inner product computation in selective data sharing setting has not been fully considered. For this fact, we propose a verifiable inner product computation scheme based on Inner Product Functional Encryption (IPFE). IPFE is employed to preserve the outsourced data privacy and restrict the computation on the outsourced data to be inner product. To achieve the key privacy and result privacy, we transform the secret key into blinded form, which in turn results in a blinded result. With the aim of implementing access control over the data user and outsourced data, we design to let cloud server perform the authentication procedures before computing inner product. This can also eliminate most computational overhead resulting from the unauthorized data user and undesired data. As a result, only the authorized data user can obtain the inner product computed on the designated outsourced data. The proposed scheme is proved to be secure under the authentication model and the result unforgeability model. The performance evaluation shows that the proposed scheme is feasible. To achieve a better security level, the proposed scheme is extended to be secure against the corrupted cloud server.

Multi-matrix verifiable computation

The problem of securely outsourcing computation to cloud servers has attracted a large amount of attention in recent years. The verifiable computation of Gennaro, Gentry, Parno (Crypto'10) allows a client to verify the server's computation of a function with substantially less time than performing the outsourced computation from scratch. In a multi-function model (Parno, Raykova, Vaikuntanathan; TCC'12) of verifiable computation, the process of encoding function and the process of preparing input are decoupled such that any client can freely submit a computation request on its input, without having to generate an encoding of the function in advance. In this paper, we propose a multi-matrix verifiable computation scheme that allows the secure outsourcing of the matrix functions over a finite field. Our scheme is outsourceable. When it is used to outsource $m$ linear functions, the scheme is roughly $m$ times faster and has less communication cost than the previously best known scheme by Fiore and Gennaro (CCS'12), both in the client-side computation and in the server-side computation. We also show the cost saving with detailed implementations.

Efficient and verifiable outsourcing computation of large-scale nonlinear programming

Efficient and verifiable outsourcing computation of large-scale nonlinear programming

Achieving Privacy-Preserving and Verifiable Data Sharing in Vehicular Fog With Blockchain

Vehicular sensing is advocated to perform data collection by exploiting a plethora of vehicular on-board sensors; meanwhile, with the merging of vehicular sensing and fog computing, the deployed road side units (RSUs) can act as fog nodes to collect and share vehicular sensory data at the network edge. However, there are still several problems in terms of the secure and reliable sharing of sensory data in vehicular fog. To resolve these issues, in this paper, we present an efficient, privacy-preserving and verifiable sensory data collection and sharing scheme with a permissioned blockchain in vehicular fog. During the data collection phase, by combining the homomorphic 2-DNF (Disjunctive Normal Form) cryptosystem and an identity-based signcryption scheme, our proposed scheme achieves the secure and verifiable computation of the average and variance of the collected vehicular sensory data. Meanwhile, to achieve efficient and reliable data sharing, we exploit a permissioned blockchain to maintain an immutable and tamper-proof record of the derived sensory data. Security analysis demonstrates the security properties of the proposed scheme, in terms of location privacy preservation, verifiability and immutability. Performance evaluations are conducted to validate the efficiency of the proposed scheme, i.e., improvements in computation and communication efficiency in comparison with a scheme without exploiting blockchain.

Verifiable secure computation of linear fractional programming using certificate validation

Outsourcing of scientic computations is attracting increasing attention since it enables the customers with limited computing resource and storage devices to outsource the sophisticated computation workloads into powerful service providers. However, it also comes up with some security and privacy concerns and challenges, such as the input and output privacy of the customers, and cheating behaviors of the cloud. Motivated by these issues, this paper focused on privacy-preserving Linear Fractional Programming (LFP) as a typical and practically relevant case for veriable secure multiparty computation. We will investigate the secure and veriable schema with correctness guarantees, by using normal multiparty techniques to compute the result of a computation and then using veriable techniques only to verify that this result was correct.

Fair payments for verifiable cloud services using smart contracts

With the advent of cloud computing, outsourcing a computation has become a common practice. A client, to have greater confidence in computations performed by the cloud, should be able to verify the correctness of the results returned. Two approaches are followed to verify the correctness of the results: (1) Proof-based verifiable computing and (2) Replication-based Verifiable Computing. The first approach uses cryptography techniques, whereas the second approach follows game-theoretic methods. Although both approaches are almost perfect solutions to verify the results, they do not discuss fairness in verifiable computing.In this paper, we consider the problem of fairness in verifiable cloud computing, which means that the cloud gets the payment from a client for an outsourced computation if and only if the client receives the correct output of the computation. Most of the existing solutions rely on a trusted third-party to realise fairness. Motivated by the recent advances in blockchain technology and smart contracts, we propose protocols for different verifiable computing techniques using smart contracts. We first present a smart-contract based solution for fair proof-based verifiable computation and show that the overhead of using smart-contract is almost negligible when both client and cloud are honest. Then we show two different solutions depending upon the number of clouds hired to achieve fairness in replication-based verifiable computing. We have designed our protocols in the Blockchain model of cryptography and proved their security under universally composable theory. We also show the financial and transactional cost analysis of proposed contracts by implementing them in solidity and running them on Ethereum Blockchain.

Practical Verifiable Computation by Using a Hardware-Based Correct Execution Environment

The verifiable computation paradigm has been studied extensively as a means to verifying the result of outsourced computation. In said scheme, the verifier requests computation from the prover and verifies the result by checking the output and proof received from the prover. Although they have great potential for various critical applications, verifiable computations have not been widely used in practice, because of their significant performance overhead. Existing cryptography-based approaches incur significant overhead, because a cryptography-based mathematical frame needs to be constructed, which prevents deviation from the correct computation. The proposed approach is to reduce the overhead by trusting the computing hardware platform where the computation is outsourced. If one trusts the hardware to do the computation, the hardware can take the place of the cryptographic computing frame, thereby guaranteeing correct computation. The key challenge of this approach is to define what exactly the hardware should guarantee for verifiable computation. For this, we introduce the concept of Correct Execution Environment (CEE), which guarantees instruction correctness and state preservation. We prove that these two requirements are satisfactory conditions for a correct output. By employing a CEE, the verifiable computation scheme can be simplified, and its overhead can be reduced drastically. The presented experimental results demonstrate that the execution time is approximately 1.7 million times faster and the verification time over 50 times faster than a state-of-the-art cryptographic approach.

A Blockchain-Assisted Verifiable Outsourced Attribute-Based Signcryption Scheme for EHRs Sharing in the Cloud

The sharing of electronic health records (EHRs) has shown great advantages in the accurate treatment of patients and the development of medical institutions. However, it is easy to cause some security problems in the process of medical data sharing. Generally, after a patient's EHRs are generated by different medical institutions, they are outsourced to the cloud server (CS) by the authorized medical institutions for storage, which causes the patient to lose control of EHRs. Moreover, malicious medical institutions and semi-trusted cloud servers may collude to tamper with EHRs to seek benefits, which threatens the integrity of EHRs. Therefore, we propose a blockchain-assisted verifiable outsourced attribute-based signcryption scheme (BVOABSC) which realizes the secure sharing of EHRs in a multi-authority cloud storge environment. Firstly, we use the attribute-based signcryption algorithm to realize the confidentiality and unforgeability of the EHRs and protect the privacy of the signer. Secondly, it greatly reduces the computational burden of users by using verifiable outsourcing computation mechanism. Most of the designcryption calculation is performed by the cloud server, and the correctness of the generated partial designcryption ciphertext is verified by users. Furthermore, we use blockchain technology to protect outsourced EHRs from tampering by illegal users. Specifically, each operation on outsourced EHRs is stored as a transaction on the public blockchain, which ensures that EHRs cannot be modified. At the same time, the auditor can verify the integrity of the outsourced EHRs by checking the corresponding transactions. In addition, the smart contract created by the patient can solve the problems in cloud storage, such as tampering EHRs and returning incorrect results. Finally, security analysis and performance evaluation show that the proposed BVOABSC scheme satisfies stronger security and higher efficiency than similar schemes.

Verifiable Quantum Cloud Computation Scheme Based on Blind Computation

In this paper, we propose a verifiable quantum cloud computation scheme based on blind quantum computation which effectively solves the privacy and verifiability problem for clients when interfacing with quantum computer in cloud computation. Different from most of present works (e.g. using brickwork state as resource state), we use cluster state with grid distributed structure to realize the universal and cryptographic calculation which is more suitable for the distributed architecture of cloud computation. Throughout the process, the random key is always held by the client that effectively promote the confidentiality. Moreover, we propose a new method to make the client Alice verifies the correctness of the results through only classical calculation. Security analysis shows that cloud server Bob can only obtain the dimension of input state and cluster state from the calculation, but cannot obtain any information of the input, the output and the algorithm. Dishonest Bob will be detected during the verification.

How to Extract Image Features Based on Co-Occurrence Matrix Securely and Efficiently in Cloud Computing

High-dimensional feature extraction based on co-occurrence matrix improves the detection performance of steganalysis, but it is difficult to be realized for massive image data by an analyzer with limited computational ability. We solve this problem by verifiable outsourcing computation, which allows a computationally weak client to outsource the evaluation of a function to a powerful but untrusted server. In this paper, we propose a verifiable outsourcing scheme of feature extraction based on co-occurrence matrix with single untrusted cloud server. The original images are protected from the server by using a projection of one to many with trapdoor, which can be realized by a symmetric probabilistic encryption scheme we present. The analyzer can obtain true results of feature extraction and detect any failure with a probability of 1 if the server misbehaves. Finally, we provide the simulations on the outsourcing of extracting ccJRM features in cloud computing. The theory analysis and experiment result also show that the proposed outsourcing scheme could greatly decrease the computation cost of the analyzer without exposure of the original images and extraction results.

Protecting data privacy in publicly verifiable delegation of matrix and polynomial functions

Outsourcing computation has gained significant attention in recent years in particular due to the prevalence of cloud computing. There are two main security concerns in outsourcing computation: guaranteeing that the server performs the computation correctly, and protecting the privacy of the client's data. The verifiable computation of Gennaro, Gentry and Parno addresses both concerns for outsourcing the computation of a function f on an input x to the cloud. The GGP scheme is privately delegatable, privately verifiable, and based on the expensive cryptographic primitives such as fully homomorphic encryption (FHE). In this paper we consider the problem of outsourcing matrix-vector multiplications of the form Fxwhere F is a matrix and xis a column vector, and construct publicly delegatable and publicly verifiable schemes. Our schemes are either input private or function private, highly efficient, and provably secure under the well-established assumptions such as the discrete-logarithm assumption. We decompose a polynomial computation, such as computing a univariate polynomial of arbitrary degree, a bivariate polynomial of arbitrary degree, a quadratic multivariate polynomial, and in general any multivariate polynomial, into a two-step computation in which the computaionally expensive step is a matrix-vector multiplication. We use the matrix schemes to outsource the computation of high-degree polynomials and obtain the first high-degree polynomial outsourcing schemes that simultaneously have public delegation, public verification and input privacy/function privacy.

Arbitrable blind quantum computation

Blind quantum computation (of a single-server case) is a two-party cryptographic protocol which involves a quantum computation server Bob and a client Alice who wants to delegate her quantum computation to Bob without revealing her quantum algorithms and her input to and output from the algorithms. Since Bob may be truant and pretend to execute some computation, Alice wants to verify Bob’s honesty on computation. To resolve this problem, the notion of the verifiability has been considered in the literature and several protocols of verifiable blind computation have been developed. Verifiable blind quantum computation enables Alice to check whether Bob is cheating or not. In addition to the above problem, another problem could arise. If Alice pretends to be a client and is actually a competitor against Bob, then she might slander Bob by fabricating his dishonesty. Therefore, if either Alice or Bob is cheating, then a “neutral” referee other than Alice and Bob should judge which is honest. The standard definition of the verifiability guarantees that only Alice can verify Bob’s computation, and thus, it should be called private verifiability. If Bob claims his innocence though he is actually cheating, then Alice cannot persuade any others that Bob is really cheating while Alice can recognize Bob’s cheating. In this paper, we incorporate arbitrators as the third party into blind quantum computation to resolve the above problems and give an arbitrable blind quantum computation scheme, which provides public verifiability in some sense.

Comments on “Publicly Verifiable Computation of Polynomials Over Outsourced Data With Multiple Sources”

With more organizational and individual data owners storing their data in the cloud, there is a corresponding need to ensure that such outsourced data can be computed by the data owners or some authorized third parties. In other words, the cloud server performs the requested computation, and returns the computation result to the requesting party. Such a paradigm is referred to as outsourced computation in the literature. A challenge is how one can ensure the correctness of the returned result, and this has been extensively studied in the literature. For example, in 2017, Song et al . proposed a protocol for publicly verifiable computation of polynomials over outsourced data with multiple sources. However, we reveal that a core building block of their protocol allows an adversary to forge the signatures on the outsourced data. Hence, this invalidates the security of the protocol. We also point out their proposal is yet very interesting and useful, only a little improvement can strengthen their proposal to be secure.

Verifiable outsourcing computation for modular exponentiation from shareable functions

Verifiable computation (VC) enables a computationally weak client to outsource the computation of a function f to a more powerful but untrusted server. The server returns an answer that allows the client to recover the correct result, accompanied by a proof of correctness. The basic requirement of a VC scheme is efficiency, i.e., the time consuming in preparing its input and verifying the server’s proof must be less than the time required to compute the function on its own. In this paper, we propose a novel outsourcing scheme for modular exponentiation from shareable functions, which is secure even in the presence of adaptive adversaries. Compared with previous works, our algorithm is superior in both efficiency and checkability. In order to keep the exponent privacy, our algorithm invokes the less subroutine, which accounts for the largest proportion of the time spent. The client can detect the error with overwhelming probability. We then gave a comparation that demonstrates the efficiency of the proposed outsourcing algorithm and scheme. Finally, we propose a generic scheme for shareable function family, and analyze the concrete security.

A secure regenerating code‐based cloud storage with efficient integrity verification

SummaryCloud storage is gaining popularity as it relieves the data owners from the burden of data storage and maintenance cost. However, outsourcing data to third‐party cloud servers raise several concerns such as data availability, confidentiality, and integrity. Recently, regenerating codes have gained popularity because of their low repair bandwidth while ensuring data availability. In this paper, we propose a secure regenerating code‐based cloud storage (SRCCS) scheme, which utilizes the verifiable computation property of homomorphic encryption scheme to check the integrity of outsourced data. In this work, an error‐correcting code (ECC)–based homomorphic encryption scheme (HES) is employed to simultaneously provide data privacy as well as error correction while supporting efficient integrity verification. In SRCCS, server regeneration process is initiated on detection of data corruption events in order to ensure data availability. The ECC‐based HES significantly reduces the probability of server regeneration and minimizes the repair cost. Extensive theoretical analysis and simulation results validate the security, efficiency, and practicability of the proposed scheme.

A Verifiable Fully Homomorphic Encryption Scheme for Cloud Computing Security

Performing smart computations in a context of cloud computing and big data is highly appreciated today. It allows customers to fully benefit from cloud computing capacities (such as processing or storage) without losing confidentiality of sensitive data. Fully homomorphic encryption (FHE) is a smart category of encryption schemes that enables working with the data in its encrypted form. It permits us to preserve confidentiality of our sensible data and to benefit from cloud computing capabilities. While FHE is combined with verifiable computation, it offers efficient procedures for outsourcing computations over encrypted data to a remote, but non-trusted, cloud server. The resulting scheme is called Verifiable Fully Homomorphic Encryption (VFHE). Currently, it has been demonstrated by many existing schemes that the theory is feasible but the efficiency needs to be dramatically improved in order to make it usable for real applications. One subtle difficulty is how to efficiently handle the noise. This paper aims to introduce an efficient and symmetric verifiable FHE based on a new mathematic structure that is noise free. In our encryption scheme, the noise is constant and does not depend on homomorphic evaluation of ciphertexts. The homomorphy of our scheme is obtained from simple matrix operations (addition and multiplication). The running time of the multiplication operation of our encryption scheme in a cloud environment has an order of a few milliseconds.

Towards dependable and trustworthy outsourced computing: A comprehensive survey and tutorial

Cloud computing provides the clients with diversified services in a flexible manner. Recently, the cloud platforms have been the basic underling-support for The IoT and mobile computing. The client outsources data storage or computation overhead to the cloud, which accordingly yields a new computing paradigm – the outsourced computing. In such a scenario, the clients hope to acquire the service quality, and wish to not leak their sensitive data to the cloud service provider. Thus, the trustworthy (verifiability) and privacy has been a hot issue for outsourced computing. In this survey, we systematically present the cryptographic methods for ensuring verifiability and privacy. We first describe the research advancement in verifiable computing and the cryptographic primitives for privacy-preserving techniques; and then, taking outsourcing cryptographic operations as an example, to show how them primitives can be integrated to achieve a dependable and privacy-preserving outsourced computing scheme. This paper bridges the gap between the theoretical cryptographic research and engineering secure cloud computing systems.

Verifiable Subgraph Matching With Cryptographic Accumulators in Cloud Computing

Due to the rapid development of social networks, bio-informatics, internet-of-things etc. , subgraph matching query can be found in various applications. Meanwhile, the increasing popularity of storing graph data in the cloud drives demands for graph query processing on a remote cloud server. However, the query results in this scenario may not be guaranteed to be correct, especially when the cloud service provider (CSP) is malicious or compromised by some adversaries, for example, a CSP might omit some edges of the graph so that its search cost would be substantially reduced. Besides, various software bugs and unintended errors are also inevitable. All current generic verifiable computation (VC) schemes applied in this scenario are not only too impractical to be implemented but also need a lot of space to locally store their auxiliary data. To that end, we have put forth both public and designated verification schemes which focus on subgraph matching problems for outsourced graph data. They utilize a modified cryptographic primitive called accumulator to realize fast verification and low local storage overhead. In addition to the two main constructions, we have proposed an optimization to make the scheme more applicable, namely, supporting dynamic updates of the graph. At last, rigorous security proofs and efficiency analysis are given, which justify that our proposed schemes are secure and efficient, satisfying the requirements of general verifiable computation protocols.