Blockchain-based verifiable computation with optimized resource allocation

Nowadays,the data that users need to calculate and process increases sharply,however,ordinary users usually lack the required capability.Therefore,resorting to outsourcing computation,they can delegate computing tasks to high-performance nodes over the network to meet their needs.In order to ensure the correctness of outsourcing computations,a verifiable computing scheme based on the blockchain smart contract is proposed,where the primary node and the replica nodes complete the task calculation and verification respectively,and reach a final consensus on the results.Moreover,the computing resources and energy consumption of each node to make the consensus are analyzed,based on which an optimization of resources allocation is proposed to maximize the transaction throughput.The simulation results show the effectiveness of the proposed scheme built on distributed consensus and also the throughput improvement by optimizing.

Analysis and improvement of verifiable blind quantum computation

In blind quantum computation(BQC),a client with weak quantum computation capabilities is allowed to delegate its quantum computation tasks to a server with powerful quantum computation capabilities,and the inputs,algorithms and outputs of the quantum computation are confidential to the server.Verifiability refers to the ability of the client to verify with a certain probability whether the server has executed the protocol correctly and can be realized by introducing trap qubits into the computation graph state to detect server deception.The existing verifiable universal BQC protocols are analyzed and compared in detail.The XTH protocol(proposed by Xu Q S,Tan X Q,Huang R in 2020),a recent improvement protocol of verifiable universal BQC,uses a sandglass-like graph state to further decrease resource expenditure and enhance verification capability.However,the XTH protocol has two shortcomings:limitations in the coloring scheme and a high probability of accepting an incorrect computation result.In this paper,we present an improved version of the XTH protocol,which revises the limitations of the original coloring scheme and further improves the verification ability.The analysis demonstrates that the resource expenditure is the same as for the XTH protocol,while the probability of accepting the wrong computation result is reduced from the original minimum(0.866)^(d*)to(0.819)^(d^(*)),where d;is the number of repeated executions of the protocol.

Blind quantum computation with a client performing different single-qubit gates

In the field of single-server blind quantum computation(BQC), a major focus is to make the client as classical as possible. To achieve this goal, we propose two single-server BQC protocols to achieve verifiable universal quantum computation. In these two protocols, the client only needs to perform either the gate T(in the first protocol) or the gates H and X(in the second protocol). With assistance from a single server, the client can utilize his quantum capabilities to generate some single-qubit states while keeping the actual state of these qubits confidential from others. By using these single-qubit states, the verifiable universal quantum computation can be achieved.

The classification of bi-quintic parametric polynomial minimal surfaces

Parametric polynomial surface is a fundamental element in CAD systems. Since the most of the classic minimal surfaces are represented by non-parametric polynomial, it is interesting to study the minimal surfaces represented in parametric polynomial form. Recently,Ganchev presented the canonical principal parameters for minimal surfaces. The normal curvature of a minimal surface expressed in these parameters determines completely the surface up to a position in the space. Based on this result, in this paper, we study the bi-quintic isothermal minimal surfaces. According to the condition that any minimal isothermal surface is harmonic,we can acquire the relationship of some control points must satisfy. Follow up, we obtain two holomorphic functions f（z） and g（z） which give the Weierstrass representation of the minimal surface. Under the constrains that the minimal surface is bi-quintic, f（z） and g（z） can be divided into two cases. One case is that f（z） is a constant and g（z） is a quadratic polynomial, and another case is that the degree of f（z） and g（z） are 2 and 1 respectively. For these two cases,we transfer the isothermal parameter to canonical principal parameter, and then compute their normal curvatures and analyze the properties of the corresponding minimal surfaces. Moreover,we study some geometric properties of the bi-quintic harmonic surfaces based on the B′ezier representation. Finally, some numerical examples are demonstrated to verify our results.

Primitives towards verifiable computation： a survey

Verifiable computation （VC） paradigm has got the captivation that in real term is highlighted by the concept of third party computation. In more explicate terms, VC allows resource constrained clients/organizations to securely outsource expensive computations to untrusted service providers, while acquiring the publicly or privately verifiable results. Many mainstream solutions have been proposed to address the diverse problems within the VC domain. Some of them imposed assumptions over performed computations, while the others took advantage of interactivity /non-interactivity, zero knowledge proofs, and arguments. Further proposals utilized the powers of probabilistic checkable or computationally sound proofs. In this survey, we present a chronological study and classify the VC proposals based on their adopted domains. First, we provide a broader overview of the theoretical advancements while critically analyzing them. Subsequently, we present a comprehensive view of their utilization in the state of the art VC approaches. Moreover, a brief overview of recent proof based VC systems is also presented that lifted up the VC domain to the verge of practicality. We use the presented study and reviewed resuits to identify the similarities and alterations, modifications, and hybridization of different approaches, while comparing their advantages and reporting their overheads. Finally, we discuss implementation of such VC based systems, their applications, and the likely future directions.