- 學位論文
全同態加密運用在解決GSM單向認證問題及效率分析
Solving the Problem of the GSM One-Way Authentication using Fully Homomorphic Encryption and Efficiency Analysis
摘要
“全同態加密”(Fully Homomorphic Encryption (FHE))是西元2009年由Gentry所提出的。FHE可以讓加密之後的密文執行兩種或是多種特定的運算，再將其解密，可得對應的明文運算結果，期間必須可以處理大量的資料並且保護其資料隱私性使其無洩漏之虞。也因為上述特點，可使得FHE可以被廣泛應用在雲端資料庫(Cloud Database)或是相等性驗證上。然而在GSM加密系統中，採用單向認證(One-way Authentication)，SIM卡將產生出來的驗證碼(signal response (SRES))傳送到認證中心，比對是否與認證中心產生出來的認證碼相同。此時，用戶端無法得知所傳送出去的認證碼是否真的傳送到正確的認證中心。在這篇論文中，我們解決了上述問題，並提供加密演算法的安全性及效率分析。因此，本文所提出結合FHE的方案將可以變得更安全、更實用。
關鍵字
全同態加密並列摘要
Gentry proposed the first practical scheme which can compute arbitrary functions of encrypted data in 2009. This scheme is named “Fully Homomorphic Encryption (FHE).” FHE allows us to compute more than two specific calculations without the secret decryption key. FHE can deal with and protect large amount of private data and can be widely used in cloud database application or data storage application. However, the GSM encryption system uses one-way authentication, SIM card will use secret key (ki) and random number (RAND) to produce a “signal response (SRES)” and send to the authentication center. At the same time, authentication center also uses ki and RAND to produce an SRES and compares two SRESs. If two SRESs are the same, authentication will succeed. If the authentication center is fake, the user can not recognize when the authentication center requests the user to send the SRES. In this thesis, we address the problem above and provide an encryption algorithm efficiency analysis. As a result, our scheme which is combined with fully homomorphic encryption is more secure and practical.