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The decentralization of blockchain can easily lead to the leakage of users’ private data at the transaction layer,which in turn leads to information security issues.The zero-knowledge range proof is designed to confidentially verify that the transaction data belongs to a legal positive integer range without revealing the transaction data.It effectively solves the problem of blockchain privacy leakage.The existing blockchain range proof scheme can still be further optimized in terms of proof speed,verification speed and calculation cost.In addition,the existing solutions cannot handle the floating-point number problem,thus limiting the application fields of range proofs.This paper proposes an efficient range proof scheme with constant computational cost and universal for floating-point numbers and integers,ZKFERP.It improves the zero-knowledge protocol based on Bulletproofs to optimize the proof structure,and a Lagrangian inner product vector generation method is designed to make the witness generation time constant and the commitment is constructed according to the floating-point number range relationship to implement floating-point range proof.ZKFERP only relies on the discrete logarithm assumption,and third-party credibility is not required.The communication cost and time complexity of ZKFERP are constant.Experimental results show that,compared with the most advanced known range proof scheme,ZKFERP’s proof speed is increased by 40.0%,and the verification speed is increased by 29.8%.

The field of visual search has gained significant attention recently, particularly in the context of web search engines and e-commerce product search platforms. However, the abundance of web images presents a challenge for modern image retrieval systems, as they need to find both relevant and diverse images that maximize users' satisfaction. In response to this challenge, we propose a non-dominated visual diversity re-ranking (NDVDR) method based on the concept of Pareto optimality. To begin with, we employ a fast binary hashing method as a coarse-grained retrieval procedure. This allows us to efficiently obtain a subset of candidate images for subsequent re-ranking. Fed with this initial retrieved image results, the NDVDR performs a fine-grained re-ranking procedure for boosting both relevance and visual diversity among the top-ranked images. Recognizing the inherent conflict nature between the objectives of relevance and diversity, the reranking procedure is simulated as the analytical stage of a multi-criteria decision-making process, seeking the optimal tradeoff between the two conflicting objectives within the initial retrieved images. In particular, a non-dominated sorting mechanism is devised that produces Pareto non-dominated hierarchies among images based on the Pareto dominance relation. Additionally, two novel measures are introduced for the effective characterization of the relevance and diversity scores among different images. We conduct experiments on three popular real-world image datasets and compare our re-ranking method with several state-of-the-art image search re-ranking methods. The experimental results validate that our re-ranking approach guarantees retrieval accuracy while simultaneously boosting diversity among the top-ranked images. [ABSTRACT FROM AUTHOR]