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  • Open Access

    ARTICLE

    Polynomial Commitment in a Verkle Tree Based on a Non-Positional Polynomial Notation

    Kunbolat T. Algazy1, Kairat S. Sakan1,2,*, Saule E. Nyssanbayeva1,2, Ardabek Khompysh1,3

    CMC-Computers, Materials & Continua, Vol.84, No.1, pp. 1581-1595, 2025, DOI:10.32604/cmc.2025.065085 - 09 June 2025

    Abstract This paper examines the application of the Verkle tree—an efficient data structure that leverages commitments and a novel proof technique in cryptographic solutions. Unlike traditional Merkle trees, the Verkle tree significantly reduces signature size by utilizing polynomial and vector commitments. Compact proofs also accelerate the verification process, reducing computational overhead, which makes Verkle trees particularly useful. The study proposes a new approach based on a non-positional polynomial notation (NPN) employing the Chinese Remainder Theorem (CRT). CRT enables efficient data representation and verification by decomposing data into smaller, independent components, simplifying computations, reducing overhead, and enhancing… More >

  • Open Access

    ARTICLE

    Distributed Secure Storage Scheme Based on Sharding Blockchain

    Jin Wang1,2, Chenchen Han1, Xiaofeng Yu3,*, Yongjun Ren4, R. Simon Sherratt5

    CMC-Computers, Materials & Continua, Vol.70, No.3, pp. 4485-4502, 2022, DOI:10.32604/cmc.2022.020648 - 11 October 2021

    Abstract Distributed storage can store data in multiple devices or servers to improve data security. However, in today's explosive growth of network data, traditional distributed storage scheme is faced with some severe challenges such as insufficient performance, data tampering, and data lose. A distributed storage scheme based on blockchain has been proposed to improve security and efficiency of traditional distributed storage. Under this scheme, the following improvements have been made in this paper. This paper first analyzes the problems faced by distributed storage. Then proposed to build a new distributed storage blockchain scheme with sharding blockchain.… More >

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