簽章驗證通常包含許多複雜且耗時之運算，為了促進驗證效率，驗證者可採取某些機制輔助，以減少驗證時之線上運算量。其中最為著名的驗證加速機制分別為批次驗證，與伺服器輔助驗證。批次驗證之概念為將簽章整批處理，期望能達到比將簽章依次處理而更佳的驗證速度。伺服器輔助驗證之概念為，將驗証者所需之部分運算量，交由一計算能力更為強大的伺服器協助計算，以減輕驗證者之運算負擔。然而此兩種機制於設計時皆須謹慎考量，以避免降低原本簽章系統之安全性。本論文分別針對批次驗證及伺服器輔助驗證，提出安全性分析並且加以深入討論，指出其安全考量上之重要性。 Signature verification involves time-consuming operations. There are two mechanisms supposed to accelerate signature verification. One is batch verification, and the other is server-aided verification. Batch verification aims to verify signatures in a batch to reduce re-operations. Server-aided verification aims to delegate part of computational load to a powerful but untrusted server to ease the on-line computational burden. Both of the two mechanisms should carefully avoid violating the security guarantee of the original signature schemes. In the thesis the cryptanalysis on both batch verification and server-aided verification is provided with the security notions.
