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<p>Multi-key fully homomorphic encryption (MKFHE) is a crucial research topic in cryptography. It allows for complex calculations on encrypted data and supports joint decryption, effectively addressing privacy protection issues. This paper introduces an improved MKFHE scheme based on BGV-type scheme LZY19+. Unlike LZY19+, which combines RGSW and RBGV to generate evaluation keys, the proposed scheme simplifies this process by introducing an intermediate vector. This modification reduces both the size and computational complexity of the evaluation keyS, significantly enhancing computational efficiency. Although LZY19+ and similar schemes require multiple rounds of complex matrix computations to generate evaluation keys, the new scheme minimizes this overhead. Additionally, the directional decryption mechanism from LZY19+ is incorporated to mitigate security risks related to the misuse or leakage of decryption keys, thereby strengthening system security. The new scheme is integrated with blockchain technology, where smart contracts automate the key distribution process. The decentralized nature of the blockchain enhances the privacy of keys during encryption while also improving the resilience of the system to attacks. Furthermore, the immutability and transparency of the blockchain ensure data integrity and traceability, further strengthening the security of the system. A comprehensive security analysis confirms that the scheme meets the IND-CPA security standard. Performance evaluation results show that the algorithm reduces the complexity of calculating the evaluation keys to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10586_2025_5486_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(O(k^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>k</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, eliminating the need for a complex evaluation keys generation process.</p>

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Research on multi-key fully homomorphic encryption algorithms suitable for blockchain

  • 期刊论文

  • 发表日期：

    2025年9月19日

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  • Yongbin Zhao,
  • Cong Men

摘要

Multi-key fully homomorphic encryption (MKFHE) is a crucial research topic in cryptography. It allows for complex calculations on encrypted data and supports joint decryption, effectively addressing privacy protection issues. This paper introduces an improved MKFHE scheme based on BGV-type scheme LZY19+. Unlike LZY19+, which combines RGSW and RBGV to generate evaluation keys, the proposed scheme simplifies this process by introducing an intermediate vector. This modification reduces both the size and computational complexity of the evaluation keyS, significantly enhancing computational efficiency. Although LZY19+ and similar schemes require multiple rounds of complex matrix computations to generate evaluation keys, the new scheme minimizes this overhead. Additionally, the directional decryption mechanism from LZY19+ is incorporated to mitigate security risks related to the misuse or leakage of decryption keys, thereby strengthening system security. The new scheme is integrated with blockchain technology, where smart contracts automate the key distribution process. The decentralized nature of the blockchain enhances the privacy of keys during encryption while also improving the resilience of the system to attacks. Furthermore, the immutability and transparency of the blockchain ensure data integrity and traceability, further strengthening the security of the system. A comprehensive security analysis confirms that the scheme meets the IND-CPA security standard. Performance evaluation results show that the algorithm reduces the complexity of calculating the evaluation keys to \(O(k^2)\) O ( k 2 ) , eliminating the need for a complex evaluation keys generation process.