In cloud computing, data processing is delegated to a remote party for efficiency and flexibility reasons. A practical user requirement usually is that the confidentiality and integrity of data processing needs to be protected. In the common scenarios of cloud computing today, this can only be achieved by assuming that the remote party does not in any form act maliciously. In this paper, we propose an approach that avoids having to trust a single entity. Our approach is based on two concepts: (1) the technical abstraction of sealed computation, i.e., a technical mechanism to confine the processing of data within a tamper-proof hardware container, and (2) the additional role of an auditing party that itself cannot add functionality to the system but is able to check whether the system (including the mechanism for sealed computation) works as expected. We discuss the abstract technical and procedural requirements of these concepts and explain how they can be applied in practice.
A trustworthy and privacy-preserving cloud may be addressed by the use of cryptographic techniques such as fully homomorphic encryption (FHE) @cite_9 . However, it is still inefficient for most computations @cite_16 . Similarly in verifiable computing @cite_8 , it was designed to enable result correctness verification but has not shown support for general purpose cloud computing yet.
@cite_9 @cite_16 @cite_8
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The rise of machine learning as a service multiplies scenarios where one faces a privacy dilemma: either sensitive user data must be revealed to the entity that evaluates the cognitive model (e.g., in the Cloud), or the model itself must be revealed to the user so that the evaluation can take place locally. Fully Homomorphic Encryption (FHE) offers an elegant way to reconcile these conflicting interests in the Cloud-based scenario and also preserve non-interactivity. However, due to the inefficiency of existing FHE schemes, most applications prefer to use Somewhat Homomorphic Encryption (SHE), where the complexity of the computation to be performed has to be known in advance, and the efficiency of the scheme depends on this global complexity. We propose a new cryptographic primitive called Delegatable Homomorphic Encryption (DHE). This allows a Trusted Authority to control delegate the evaluation of circuits over encrypted data to untrusted workers evaluators by issuing tokens. This primitive can be both seen as a public-key counterpart to Verifiable Computation, where input generation and output verification are performed by different entities, or as a generalisation of Fully Homomorphic Encryption enabling control over computations on encrypted data. Our primitive comes with a series of extra features: 1) there is a one-time setup procedure for all circuits; 2) senders do not need to be aware of the functions which will be evaluated on the encrypted data, nor do they need to register keys; 3) tokens are independent of senders and receiver; and 4) receivers are able to verify the correctness of computation given short auxiliary information on the input data and the function, independently of the complexity of the computed circuit. We give a modular construction of such a DHE scheme from three components: Fully Homomorphic Encryption (FHE), Functional Encryption (FE), and a (customised) MAC. As a stepping stone, we first define Verifiable Functional Encryption (VFE), and then show how one can build a secure DHE scheme from a VFE and an FHE scheme. We also show how to build the required VFE from a standard FE together with a MAC scheme. All our results hold in the standard model. Finally, we show how one can build a verifiable computation (VC) scheme generically from a DHE. As a corollary, we get the first VC scheme which remains verifiable even if the attacker can observe verification results. The rapid expansion and increased popularity of cloud computing comes with no shortage of privacy concerns about outsourcing computation to semi-trusted parties. Leveraging the power of encryption, in this paper, we introduce Cryptoleq: an abstract machine based on the concept of one instruction set computer, capable of performing general-purpose computation on encrypted programs. The program operands are protected using the Paillier partially homomorphic cryptosystem, which supports addition on the encrypted domain. Full homomorphism over addition and multiplication, which is necessary for enabling general-purpose computation, is achieved by inventing a heuristically obfuscated software re-encryption module written using Cryptoleq instructions and blended into the executing program. Cryptoleq is heterogeneous, allowing mixing encrypted and unencrypted instruction operands in the same program memory space. Programming with Cryptoleq is facilitated using an enhanced assembly language that allows the development of any advanced algorithm on encrypted data sets. In our evaluation, we compare Cryptoleq's performance against a popular fully homomorphic encryption library, and demonstrate correctness using a typical private information retrieval problem. Cloud computing enables resource-constrained clients to economically outsource their huge computation workloads to a cloud server with massive computational power. This promising computing paradigm inevitably brings in new security concerns and challenges, such as input output privacy and result verifiability. Since matrix inversion computation (MIC) is a quite common scientific and engineering computational task, we are motivated to design a protocol to enable secure, robust cheating resistant, and efficient outsourcing of MIC to a malicious cloud in this paper. The main idea to protect the privacy is employing some transformations on the original matrix to get a encrypted matrix which is sent to the cloud; and then transforming the result returned from the cloud to get the correct inversion of the original matrix. Next, a randomized Monte Carlo verification algorithm with one-sided error is employed to successfully handle result verification. In this paper, the superiority of this novel technique in designing inexpensive result verification algorithm for secure outsourcing is well demonstrated. We analytically show that the proposed protocol simultaneously fulfills the goals of correctness, security, robust cheating resistance, and high-efficiency. Extensive theoretical analysis and experimental evaluation also show its high-efficiency and immediate practicability.