GSW加密方案中基於中國剩餘定理的訊息資料範圍擴展和增強型多密鑰密文大小縮減方法

Abstract

當前的GSW加密方案的用戶信息選擇範圍有限。我們提出一種基於中國餘數定理（CRT）的信息分解方法，以解決這一限制並擴大數據範圍。該方法通過啟用平行操作並在密碼學領域內更高效地管理多個同態操作，克服了現有方法的低效率。這一優勢延伸至未來的GSW多鍵情境應用。我們也研究了GSW加密方案中過大的密文問題。通過整合當前的GSW多鍵設計並適應多鍵情境的壓縮方法，我們增強了其在實際密碼系統中的適用性。具體來說，我們使用CRT方法在多鍵情境中進行同態加法操作，並改進多鍵壓縮方法。最後，我們分別在聯邦學習和多方通信框架中展示了這些優化方法在多鍵操作中的性能，凸顯了我們方法在實際密碼學應用中的實用潛力。

The current GSW encryption scheme has a limited range of user message options. We propose a message decomposition method based on the Chinese Remainder Theorem (CRT) to address this limitation and expand the data scope. This approach overcomes the inefficiencies of existing methods by enabling parallel operations and managing multiple homomorphic operations more efficiently within the cryptographic domain. This advantage extends to future applications in GSW multi-key scenarios. We also studied the issue of excessively large ciphertexts in the GSW encryption scheme. By integrating the current GSW multi-key design and adapting the compression method for multi-key scenarios, we enhance its applicability in real-world cryptosystems. Specifically, we use the CRT method to perform homomorphic addition operations in multi-key scenarios and improve the multi-key compression method. Finally, we demonstrate the performance of these optimization methods in multi-key operations using federated learning and multi-party communication frameworks, respectively, highlighting the practical potential of our methods in real-world cryptographic applications.