科技日新月異，人們在影像處理與人工智慧上的應用日漸增高，而這些應用都需要消耗大量的電腦資源，因此人們將應用拓展至雲端上，並利用基於網際網路傳送資訊的雲端運算，並在不消耗電腦資源的情況下進行大量的算術運算。網際網路能使人們更簡單地使用雲端資源，但同時背後也隱藏著各種資安問題，因此本論文利用以不存在可信第三方為基礎下進行的加密演算法—安全多方計算，與能辨識資料的正確性與否的演算法—錯誤更正，建構一個類似分散式運算的系統。利用秘密分享的特性，在過程中不使用特定金鑰進行資料的保密，藉此降低他人竊取重要資訊的可能性，並將兩種演算法應用於影像強化與卷積神經網路中。在應用於影像強化的過程中，除了一般的實數域運算外，更是將其運用於保密性更高的整數域運算中，並探討加密演算法在各個運算下的同態性質是否存在與討論非線性運算下如何消除誤差所導致的圖片失真問題；在卷積神經網路的實數域應用中，亦探討各個運算下的同態性質存在與否，且討論並歸納出最適合的秘密重建方式，使得在非線性運算下進行積神經網路運算仍可以正確地重建秘密，並得到重建率高達90%以上的預測模型系統。最後，在利用秘密分享與錯誤更正演算法的基礎下，本論文結合雲端運算完成影像強化與卷積神經網路的加解密系統實現。

With the rapid development of technology, the needs for applications in image processing and artificial intelligence are increasing day by day. People need to require high-quality processors that can perform high computations. But with the continuous progress in technology, simply speeding up computations is not enough for the situation. Therefore, people use the cloud with cloud computing which is based on the Internet and performs high-quality computation without consuming local computer resources. However, when people use the internet free, the issue of information security appears gradually. In this thesis, we will use an encryption algorithm based on the absence of a trusted third party—Secure Multi-Party Computation (SMPC) which does not use the specific keys or methods to maintain the data confidentiality and also use the Berlekamp-Welch algorithm for error detection/correction to make sure the correction of the information. Further, we will apply the proposed algorithms to image enhancement and convolution neural networks, and discuss the homomorphism in the algorithms, and implement the system with cloud computing.

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