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Testing quantum circuits and detecting insecure encryption, 2011; http://arxiv.org/ abs/1108.1052
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Symmetric quantum fully homomorphic encryption with perfect security. arXiv: 1304.5087
"... Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic enc ..."
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Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic encryption (QHE) and quantum fully homomorphic encryption (QFHE). Then we construct a symmetric QFHE scheme based on quantum onetime pad. This scheme permits any unitary transformation on any nqubit state that has been encrypted. Compared with classical homomorphic encryption, the QFHE scheme has perfect security.
Computational Distinguishability of Quantum Channels
, 2009
"... The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the wellknown satisfiability problem from classical to quantum computation. This problem is shown to be surprisingly hard: it is complete for the class QIP of problems that h ..."
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The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the wellknown satisfiability problem from classical to quantum computation. This problem is shown to be surprisingly hard: it is complete for the class QIP of problems that have quantum interactive proof systems, which implies that it is hard for the class PSPACE of problems solvable by a classical computation in polynomial space. Several restrictions of distinguishability are also shown to be hard. It is no easier when restricted to quantum computations of logarithmic depth, to mixedunitary channels, to degradable channels, or to antidegradable channels. These hardness results are demonstrated by finding reductions between these classes of quantum channels. These techniques have applications outside the distinguishability problem, as the construction for mixedunitary channels is used to prove that the additivity problem for the classical capacity of quantum channels can be equivalently restricted to the mixed unitary channels.
Unconditionally verifiable blind computation
, 2014
"... Blind Quantum Computing (BQC) allows a client to have a server carry out a quantum computation for them such that the client’s input, output and computation remain private. A desirable property for any BQC protocol is verification, whereby the client can verify with high probability whether the serv ..."
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Blind Quantum Computing (BQC) allows a client to have a server carry out a quantum computation for them such that the client’s input, output and computation remain private. A desirable property for any BQC protocol is verification, whereby the client can verify with high probability whether the server has followed the instructions of the protocol, or if there has been some deviation resulting in a corrupted output state. A verifiable BQC protocol can be viewed as an interactive proof system leading to consequences for complexity theory. The authors, together with Broadbent, previously proposed a universal and unconditionally secure BQC scheme where the client only needs to be able to prepare single qubits in separable states randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. In this paper we extend that protocol with new functionality allowing blind computational basis measurements, which we use to construct a new verifiable BQC protocol based on a new class of resource states. We rigorously prove that the probability of failing to detect an incorrect output is exponentially small in a security parameter, while resource overhead remains polynomial in this parameter. The new resource state allows entangling gates to be performed between arbitrary pairs of logical qubits with only constant overhead. This is a significant improvement on the original scheme, which required that all computations to be performed must first be put into a nearest neighbour form, incurring linear overhead in the number of qubits. Such an improvement has important consequences for efficiency and faulttolerance thresholds. 1
The quantum onetime pad . . .
"... The formula in Eq. (2) is socalled singleletter, meaning that an optimization over a single copy of the probability distribution gives the asymptotic rate. Moreover it is additive, i.e. for two probability distributions PXY Z and QX ′ Y ′ Z ′, C(PXY Z ⊗QX ′ Y ′ Z ′) = C(PXY Z)+C(QX ′ Y ′ Z ′) [6] ..."
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The formula in Eq. (2) is socalled singleletter, meaning that an optimization over a single copy of the probability distribution gives the asymptotic rate. Moreover it is additive, i.e. for two probability distributions PXY Z and QX ′ Y ′ Z ′, C(PXY Z ⊗QX ′ Y ′ Z ′) = C(PXY Z)+C(QX ′ Y ′ Z ′) [6]. We can then say that Eq. (2) completely characterizes how to optimally distill secretkey in the oneway scenario. In quantum information theory, the paradigm described above has two natural analogues, and both have been extensively analysed [10], [11], [12]. The first is to distill a secretkey from a tripartite quantum state ψABE 〉 shared by Alice, Bob and Eve [12]. Alice and Bob can perform any operation allowed by quantum mechanics on their shares of the state, while (in the oneway setting considered here) Alice can communicate public classical messages to Bob and Eve. The second is entanglement distillation [10], in which Alice and Bob wish to distill EinsteinPodolskyRosen (EPR) pairs from a shared state ψAB by local quantum operations and, again, classical communication from Alice to Bob (here too, although not needed, one can consider that an eavesdropper has a purification of ψAB i.e. a pure state ψABE such that ψAB = trEψAB, and Eve learns all the classical communication that Alice sends to Bob). In both paradigms, the shared randomness is extended from the original classical probability distribution to a quantum state. The public communication, however, remains the same; even in the quantum case only classical messages can be publicly communicated. A natural question then emerges: is there a meaningful notion of public quantum communication?
Based on Quantum Computation
"... Copyright & reuse City University London has developed City Research Online so that its users may access the research outputs of City University London's staff. Copyright © and Moral Rights for this paper are retained by the individual author(s) and / or other copyright holders. All materia ..."
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Copyright & reuse City University London has developed City Research Online so that its users may access the research outputs of City University London's staff. Copyright © and Moral Rights for this paper are retained by the individual author(s) and / or other copyright holders. All material in City Research Online is checked for eligibility for copyright before being made available in the live archive. URLs from City Research Online may be freely distributed and linked to from other web pages. Versions of research The version in City Research Online may differ from the final published version. Users are advised to check the Permanent City Research Online URL above for the status of the paper. Enquiries If you have any enquiries about any aspect of City Research Online, or if you wish to make contact with the author(s) of this paper, please email the team at publications@city.ac.uk.PEA: Polymorphic Encryption Algorithm
QUANTUM DIGITAL SIGNATURE BASED ON QUANTUM ONEWAYFUNCTIONS
"... ABSTRACT A quantum digital signature scheme based on quantum mechanics is proposed in this paper. The security of the protocol relies on the existence of quantum oneway functions by fundamental quantum principles. Our protocol involves a socalled arbitrator who validates and authenticates the sign ..."
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ABSTRACT A quantum digital signature scheme based on quantum mechanics is proposed in this paper. The security of the protocol relies on the existence of quantum oneway functions by fundamental quantum principles. Our protocol involves a socalled arbitrator who validates and authenticates the signed message. This scheme uses public quantum keys publicized by the signatory to verify the validity of the signature and uses quantum onetime pad to ensure the security of quantum information on channel. To guarantee the authenticity of the transmitted quantum states, a family of quantum stabilizer code is employed. The proposed scheme presents a novel method to construct secure quantum signature systems for future secure communications. KEY WORDS Information security; Digital signature; Quantum cryptography; Error correction code; Quantum oneway functions 1 Introduction Quantum cryptography aims at providing information security that relies on the main properties of quantum mechanics. The most successful topic of quantum cryptography is quantum key distribution (QKD), which was firstly invented by Bennett and Brassard in 1984 [1]. QKD is believed to be the first practical quantum information processor and its unconditional security has been proven [2, 3].