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  • 基于整數同態加密的定點數密態計算方案

    Fixed-point privacy-preserving computation scheme on integer homomorphic encryption

    • 摘要: 本文針對實數類型敏感數據在現實多方應用中的隱私性需求,提出了一種采用整數同態加密實現定點數密態計算的方案. 該方案通過數域轉換將有符號定點表示的實數類型數據映射為整數,進而利用多方整數全同態對轉換后的整數進行密態計算. 更重要的是,為解決定點數密態計算中的小數點漂移問題,給出了隨機小數位生成算法和小數位截斷算法,并提供了正確性與選擇明文攻擊下截斷密文的不可區分性安全的證明及分析. 對于 n 個參與者,本方案的通信復雜性 O(n^2) 和計算復雜性 O(n^3) 均不受小數位長 \gamma 影響,因而同Catrina等人方案的 O(n^2\gamma ) 和 O(n^3\gamma ) 相比,性能不會隨小數位長的增加而降低. 實驗驗證也表明本方案具有更高的效率和更好的實用性.

       

      Abstract: This study focuses on the increasingly critical privacy requirements of sensitive real-number data in modern and practical multiparty applications such as collaborative data analysis, privacy-preserving machine learning, and secure financial computations. It proposes a novel and efficient scheme for fixed-point privacy-preserving computation based on integer homomorphic encryption. Specifically, the scheme is designed to ensure both accuracy and security in scenarios where real-number data must be shared and processed among distributed parties without revealing private values. The proposed scheme works by first converting real-number data, typically represented in signed fixed-point formats, into integers through a domain translation mechanism. This translation maps real numbers into integer spaces while preserving the relative magnitude and sign information. Once this translation is performed, the scheme applies multiparty fully homomorphic encryption over integers to perform the necessary computations on the encrypted data. This approach enables secure and collaborative computation without exposing raw numerical values, making it suitable for privacy-sensitive scenarios such as healthcare or finance. A technical challenge in fixed-point computation is the problem of decimal point drift, which arises because arithmetic multiplication operations can cause uncontrolled expansion or contraction of decimal digits. To address this issue, this paper introduces a new algorithm for random decimal digit generation, which injects controlled errors to maintain semantic security, as well as an algorithm for decimal digit truncation, which ensures that results remain bounded and interpretable after computation. These algorithms are accompanied by rigorous theoretical analysis, including correctness proofs and a formal demonstration of their security properties. More importantly, this study defines and proves a new security concept called INDistinguishability under Chosen-Plaintext Attacks for TRUNCated ciphertexts (IND-CPA-TRUNC). This security definition extends the classical IND-CPA model by incorporating the characteristics of fixed-point truncation operations, which are essential for practical homomorphic computations of real-valued data. Furthermore, it is proven that under the assumption of an underlying multiparty integer fully homomorphic encryption scheme that satisfies IND-CPA security, the proposed scheme guarantees privacy in the semi-honest adversarial model. The proposed method is also scalable and efficient. For a system with n participants, the communication and computational complexities remains at O(n^2) and O(n^3), respectively, regardless of the decimal place length, which is denoted as \gamma . This is in contrast to the widely cited scheme by Catrina et al., in which both complexities scaled linearly with \gamma , resulting in O(n^2\gamma )communication and O(n^3\gamma ) computation. Therefore, the proposed scheme exhibits constant complexity with respect to \gamma , making it particularly suitable for applications that require high numerical accuracy. The study includes comprehensive experimental validation, demonstrating that the proposed scheme not only achieves higher computational efficiency but also offers better practical performance in real-world settings. This empirical evidence confirms that the scheme can be implemented feasibly in multiparty systems without significant performance degradation. In conclusion, this study makes several key contributions to the field of secure multiparty computation by combining integer homomorphic encryption with novel fixed-point arithmetic techniques and by establishing provable security guarantees. This offers a significant step forward for privacy-preserving real-number computations, particularly in settings where performance and scalability are crucial.

       

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