Classical Homomorphic Encryption for Quantum Circuits

We present the first leveled fully homomorphic encryption scheme for quantum circuits with classical keys. The scheme allows a classical client to blindly delegate a quantum computation to a quantum server: an honest server is able to run the computation while a malicious server is unable to learn any information about the computation. We show that it is possible to construct such a scheme directly from a quantum secure classical homomorphic encryption scheme with certain properties. Finally, we show that a classical homomorphic encryption scheme with the required properties can be constructed from the learning with errors problem

Experimental Demonstration of Quantum Fully Homomorphic Encryption with Application in a Two-Party Secure Protocol

A fully homomorphic encryption system hides data from unauthorized parties while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more powerful server without revealing their inputs, a fully homomorphic cryptosystem can be used as a building block in the construction of a number of cryptographic functionalities. Designing such a scheme remained an open problem until 2009, decades after the idea was first conceived, and the past few years have seen the generalization of this functionality to the world of quantum machines. Quantum schemes prior to the one implemented here were able to replicate some features in particular use cases often associated with homomorphic encryption but lacked other crucial properties, for example, relying on continual interaction to perform a computation or leaking information about the encrypted data. We present the first experimental realization of a quantum fully homomorphic encryption scheme. To demonstrate the versatility of a a quantum fully homomorphic encryption scheme, we further present a toy two-party secure computation task enabled by our scheme

Experimental Demonstration of Quantum Fully Homomorphic Encryption with Application in a Two-Party Secure Protocol

A fully homomorphic encryption system hides data from unauthorized parties while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more powerful server without revealing their inputs, a fully homomorphic cryptosystem can be used as a building block in the construction of a number of cryptographic functionalities. Designing such a scheme remained an open problem until 2009, decades after the idea was first conceived, and the past few years have seen the generalization of this functionality to the world of quantum machines. Quantum schemes prior to the one implemented here were able to replicate some features in particular use cases often associated with homomorphic encryption but lacked other crucial properties, for example, relying on continual interaction to perform a computation or leaking information about the encrypted data. We present the first experimental realization of a quantum fully homomorphic encryption scheme. To demonstrate the versatility of a a quantum fully homomorphic encryption scheme, we further present a toy two-party secure computation task enabled by our scheme

Experimental Demonstration of Quantum Fully Homomorphic Encryption with Application in a Two-Party Secure Protocol

A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more powerful server without revealing their inputs, a fully homomorphic cryptosystem can be used as a building block in the construction of a number of cryptographic functionalities. Designing such a scheme remained an open problem until 2009, decades after the idea was first conceived, and the past few years have seen the generalization of this functionality to the world of quantum machines. Quantum schemes prior to the one implemented here were able to replicate some features in particular use-cases often associated with homomorphic encryption but lacked other crucial properties, for example, relying on continual interaction to perform a computation or leaking information about the encrypted data. We present the first experimental realisation of a quantum fully homomorphic encryption scheme. We further present a toy two-party secure computation task enabled by our scheme. Finally, as part of our implementation, we also demonstrate a post-selective two-qubit linear optical controlled-phase gate with a much higher post-selection success probability (1/2) when compared to alternate implementations, e.g. with post-selective controlled-$Z$ or controlled-$X$ gates (1/9).Comment: 11 pages, 16 figures, 2 table

Ciphertext Policy Attribute based Homomorphic Encryption (CP-ABHERLWE): a fine-grained access control on outsourced cloud data computation

Recently, homomorphic encryption is becoming one of the holy grail in modern cryptography research and serve as a promising tools to protect outsourced data solutions on cloud service providers. However, most of the existing homomorphic encryption schemes are designed to achieve Fully Homomorphic Encryption that aimed to support arbitrary computations for only single-data ownership scenario. To bridge these gaps, this paper proposed a non-circuit based Ciphertext Policy-Attribute Based Homomorphic Encryption (CP-ABHER-LWE) scheme to support outsourced cloud data computations with a fine-grained access control under the multi-user scenario. First, this paper incorporates Attribute Based Encryption (ABE) scheme into homomorphic encryption scheme in order to provide a fine grained access control on encrypted data computation and storage. Then, the proposed CP-ABHER-LWE scheme is further extended into non-circuit based approach in order to increase the practical efficiency between enterprise and cloud service providers. The result shows that the non-circuit based CP-ABHER-LWE scheme has greatly reduced the computation time and ciphertext size as compared to circuit based approach. Subsequently, the proposed CP-ABHER-LWE scheme was proven secure under a selective-set model with the hardness of Decision Ring-LWEd,q,ई problem

On FHE without bootstrapping

We investigate the use of multivariate polynomials in constructing a fully homomorphic encryption. In this work we come up with two fully homomorphic schemes. First, we propose an IND-CPA secure symmetric key homomorphic encryption scheme using multivariate polynomial ring over finite fields. This scheme gives a method of constructing a CPA secure homomorphic encryption scheme from another symmetric deterministic CPA secure scheme. We base the security of the scheme on pseudo random functions and also construct an information theoretically secure variant, rather than basing security on hard problems like Ideal Membership and Gröbner basis as seen in most polly cracker based schemes which also use multivariate polynomial rings. This scheme is not compact but has many interesting properties- It can evaluate circuits of arbitrary depths without bootstrapping for bounded length input to the algorithm. Second what follows naturally is, an attempt to make it compact we propose some changes to the scheme and analyse the scheme in (Albrecht et. al. Asiacrypt-2011). We try to make it compact but fail and realise that this could give us a Multi Party Computation protocol. Realising that polynomials leads us to non compact schemes we move propose schemes based on matrices. We then propose our candidate for a fully homomorphic encryption without bootstrapping

Experimental demonstration of quantum fully homomorphic encryption with application in a two-party secure protocol

A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more powerful server without revealing their inputs, a fully homomorphic cryptosystem can be used as a building block in the construction of a number of cryptographic functionalities. Designing such a scheme remained an open problem until 2009, decades after the idea was first conceived, and the past few years have seen the generalization of this functionality to the world of quantum machines. Quantum schemes prior to the one implemented here were able to replicate some features in particular use-cases often associated with homomorphic encryption but lacked other crucial properties, for example, relying on continual interaction to perform a computation or leaking information about the encrypted data. We present the first experimental realisation of a quantum fully homomorphic encryption scheme. We further present a toy two-party secure computation task enabled by our scheme. Finally, as part of our implementation, we also demonstrate a post-selective two-qubit linear optical controlled-phase gate with a much higher post-selection success probability (1/2) when compared to alternate implementations, e.g. with post-selective controlled-Z or controlled-X gates (1/9).</p

Quantum Fully Homomorphic Encryption With Verification

Fully-homomorphic encryption (FHE) enables computation on encrypted data while maintaining secrecy. Recent research has shown that such schemes exist even for quantum computation. Given the numerous applications of classical FHE (zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is reasonable to hope that quantum FHE (or QFHE) will lead to many new results in the quantum setting. However, a crucial ingredient in almost all applications of FHE is circuit verification. Classically, verification is performed by checking a transcript of the homomorphic computation. Quantumly, this strategy is impossible due to no-cloning. This leads to an important open question: can quantum computations be delegated and verified in a non-interactive manner? In this work, we answer this question in the affirmative, by constructing a scheme for QFHE with verification (vQFHE). Our scheme provides authenticated encryption, and enables arbitrary polynomial-time quantum computations without the need of interaction between client and server. Verification is almost entirely classical; for computations that start and end with classical states, it is completely classical. As a first application, we show how to construct quantum one-time programs from classical one-time programs and vQFHE.Comment: 30 page

Threshold Fully Homomorphic Encryption and Secure Computation

Cramer, Damgård, and Nielsen~\cite{CDN01} show how to construct an efficient secure multi-party computation scheme using a threshold homomorphic encryption scheme that has four properties i) a honest-verifier zero-knowledge proof of knowledge of encrypted values, ii) proving multiplications correct iii) threshold decryption and iv) trusted shared key setup. Naor and Nissim~\cite{NN01a} show how to construct secure multi-party protocols for a function $f$ whose communication is proportional to the communication required to evaluate $f$ without security, albeit at the cost of computation that might be exponential in the description of $f$. Gentry~\cite{Gen09a} shows how to combine both ideas with fully homomorphic encryption in order to construct secure multi-party protocol that allows evaluation of a function $f$ using communication that is {\bf independent of the circuit description of $f$} and computation that is polynomial in $|f|$. This paper addresses the major drawback\u27s of Gentry\u27s approach: we eliminate the use of non-black box methods that are inherent in Naor and Nissim\u27s compiler. To do this we show how to modify the fully homomorphic encryption construction of van Dijk et al.~\cite{vDGHV10} to be threshold fully homomorphic encryption schemes. We directly construct (information theoretically) secure protocols for sharing the secret key for our threshold scheme (thereby removing the setup assumptions) and for jointly decrypting a bit. All of these constructions are constant round and we thoroughly analyze their complexity; they address requirements (iii) and (iv). The fact that the encryption scheme is fully homomorphic addresses requirement (ii). To address the need for an honest-verifier zero-knowledge proof of knowledge of encrypted values, we instead argue that a weaker solution suffices. We provide a 2-round blackbox protocol that allows us to prove knowledge of encrypted bits. Our protocol is not zero-knowledge, but it provably does not release any information about the bit being discussed, and this is sufficient to prove the correctness of a simulation in a method similar to Cramer et al. Altogether, \emph{we construct the first black-box secure multi-party computation protocol that allows evaluation of a function $f$ using communication that is independent of the circuit description of $f$}