行動網路上身份導向公鑰密碼系統之計算與應用

Abstract

在下一代的行動通訊系統中，無線資訊服務提供者(例如：行動銀行)必須發展一套安全機制來確保端點對端點之間的安全性(end-to-end security)。目前存在的端點對端點的安全機制主要是建立在公鑰密碼系統上，其中一個非常重要的議題是如何確保公鑰的認證正確性。身份導向公鑰密碼系統利用可以用來確認使用者身份的資訊來產生公鑰，進而確保所取得公鑰的認證正確性。Boneh和Franklin提出一個完整且有效率的身份導向加密系統，他們利用橢圓曲線上的一種雙線性對-威耳對(Weil pairing)來建構加解密系統，其中雙線性對的運算在整個加解密運算過程中佔相當大的份量，因此如何加速雙線性對的運算在身份導向密碼系統中是一個相當重要的議題。本論文主要研究橢圓密碼上雙線性對的特性，並提出在不同有限體上的雙線性對加速演算法，同時也提供行動通訊上有效率的端點對端點安全機制的應用。

In the next generation mobile telecommunications, any third party that provides wireless data services (e.g., mobile banking) must have its own solution for end-to-end security. Existing mobile security mechanisms are based on public-key cryptosystem. The main concern in a public-key setting is the authenticity of the public key. This issue can be resolved by identity-based (ID-based) cryptography where the public key of a user can be derived from public information that uniquely identifies the user. The first complete and efficient ID-based encryption scheme was proposed by Boneh and Franklin. They use a bilinear map (the Weil pairing) over elliptic curves to construct the encryption/decryption scheme. However, in the existing ID-based cryptosystem, the pairing computing has significant overhead. Therefore, efficient algorithm for computing bilinear pairing is essential for implementation. In this dissertation, we will study the bilinear pairings over elliptic curves and design improved algorithms for the computation of pairing over different finite fields. This will provide efficient implementations for ID-based cryptosystems in mobile devices to construct end-to-end security mechanisms.