以拉格朗日鬆弛法最佳化序列式多因子生物驗證系統 FAR 與 FRR 之上界曲線

Abstract

身份驗證在資訊安全中扮演著重要的角色，通過身份驗證，系統能夠在授予訪問權限之前確認用戶的身份。身份驗證從傳統的密碼驗證轉為生物特徵驗證，從單模態走向多模態，研究人員通過不同的方法努力提高身份驗證系統的準確性。 序列式多因子生物認證系統將多種生物特徵串聯融合，並在每個階段驗證一個生物特徵。序列式融合允許用戶提供部分生物識別模態，使其更為方便使用。此外，大部分真實用戶在第一階段即可通過驗證，而入侵者則需通過所有生物識別關卡。如此一來，辨識系統的效能與安全性得以實現。 過去的研究中，FAR × FRR = Constant 作為上界曲線大大地高估了FAR 與 FRR ，使序列式多因子生物認證系統的表現被低估。本研究提供一種有效的方法來尋找貼合資料的上界曲線，我們將問題轉為數學公式，並使用拉格朗日鬆弛方法對其進行求解，透過實驗證明更好地擬合曲線使系統產生更準確的結果，解決低估問題。此外，我們將上界曲線設定為正多項式，可以將其帶入 GP 或其他方法中。 研究結果顯示，透過拉格朗日鬆弛法，可以快速地找到具有最小誤差平方和的上界曲線，並大幅提升系統的表現。而有效的資料篩選，可以使上界曲線更貼合重要的資料點，獲得更優的系統表現。

Authentication plays an important role in information security. With authentication, the system is able to confirm the user's identity before granting the access privileges. Authentication has changed from traditional password verification to biometric authentication, and from uni-modal to multi-modal. Researchers have worked hard to improve the accuracy of authentication systems through different methods. A serial fusion multimodal biometric authentication system fuses the multi-biometric in series and verifies one biometric at each stage. By allowing users to input a subset of biometric modalities, serial fusion are more user-friendly. In addition, most genuine users can be verified in the first stage, while imposters need to pass all biometric verifications. In this way, the efficiency and security of the identification system are realized. In the preliminary work, FAR × FRR = Constant was used as the upper bounding curve which greatly overestimate FAR and FRR, so that the performance of the serial fusion multimodal biometric authentication system was underestimated. This study provides an effective method to find the upper bounding curve that fits the data. The problem is turned into a mathematical formula and solved by the Lagrangian relaxation method. Through experiments, it is proved that better fitting curves make the system produces more accurate results and addresses underestimation. In addition, the upper bounding curve is set as a posynomial, which can be brought into GP or other methods. The research shows that the upper bounding curve with the minimum sum of squared errors can be quickly found through the Lagrangian Relaxation method, and the performance of the system can be greatly improved. Effective data screening can make the upper bounding curve more closely fit important data points and obtain better system performance.