Loading...
|
Please use this identifier to cite or link to this item:
http://asiair.asia.edu.tw/ir/handle/310904400/9598
|
| Title: | 雙線性配對計算效能提升之研究 |
| Authors: | 劉兆樑 |
| Contributors: | 資訊學院
資訊多媒體應用學系 |
| Keywords: | 橢圓曲線密碼系統
雙線性配對密碼系統
Pairing計算
Miller演算法
密碼
Elliptic curve cryptosystem,
Pairing-based cryptosystem,
Pairing computation, |
| Date: | 2009 |
| Issue Date: | 2010-05-13 02:39:31 (UTC+0) |
| Abstract: | 近年隨著ID-based 密碼系統的興起，擴大了雙線性配對的應用層面。使得植基於雙
線性配對的密碼系統設計，在近代密碼學上佔有一席之地，而利用雙線性配對建構的密
碼學相關應用有：加密系統、認證式金鑰協定、數位簽章等等。時至今日，這些相關應
用更在近代密碼學研究上扮演一個重要的角色。這些密碼系統的主要特性為其所需之金
鑰長度很短，但是卻可以達到相對上的安全需求。不過Pairing 的計算仍較其他常見的
公鑰系統的相關運算複雜與費時，因此Pairing 計算效能之提升就成為這類密碼系統成
敗的關鍵。
而在Pairing-based 密碼系統中，Pairing 計算佔據最大的計算量，因此對於相關密碼
系統來說，如何加速雙線性配對函數的計算就成了一個非常重要的課題。然而第一個能
有效率計算Pairing 的演算法，是由Miller 在1986 年所提出，而直到近幾年才再有學者
利用不同之概念，提出能增進Pairing 運算效能的方法。2006 年，學者Black 等人以共
軛直線的概念提出了三種版本的演算法以改善Miller 演算法[12]，隨後我們也對Black
等人的前兩個版本提出改進方案[52]。而學者Wu 等人則利用我們的概念[80]，改進了[12]
中第三個版本之計算效率，而在執行先前計畫時，我們也使用更新之技術修正了[52]的
缺點。
因此在本計畫的第一年，我們將評估先前計畫的成果應用於Black 等人第三種版本
之可行性，並據以改善在特徵值為3 基本體之Pairing 計算效率。最後整合出一套可適
用於所有版本之有效率的Pairing 計算模式，並在完成效能分析與正確性證明後撰寫成
論文發表。
而計畫的第二年，我們將應用計畫第一年所得之成果，針對在網路環境中計算能力
受限之行動裝置，進行Pairing 計算負載之評估。在完成相關評估後設計出合於需求之
不對稱型態之Pairing 計算模式。
The rise of ID-based cryptography has led to extensive use of bilinear pairings such as
Weil pairing and Tate pairing. Since then, the design of Pairing-based cryptosystems has
been an important issue in the cryptography, such as, encryption system, key-agreement
protocol, signature scheme and so on. Henceforth, applications utilizing these pairings have
played an important role in modern cryptography. In many of these applications, the
calculation of these pairings is one of the dominant computational tasks.
However, in the existing Pairing-based cryptosystem, the pairing computing has
significant overhead. Therefore, proposing an efficient algorithm for computing bilinear
pairing is an important research issue. The first efficient algorithm for computing pairings
was proposed by Miller in 1986. Recently, in order to improve efficiency, most researches on
pairing computation have been directed at many different aspects. In 2006, Blake et al.
proposed three algorithms to improve Miller’s algorithm by the conjugate of lines [12]. In
[52], we modified the first two algorithms to reduce the computational overhead. Soon later,
Wu et al. employ our new method to propose an algorithm for computing pairing over the
ground field in characteristic 3 [80]. In the passed subject, we had improved [52] in a new
method without segmentation algorithm.
In the first subject, we will study the feasibility for employing our new method to the
BMX-3 algorithm, and implement this method for pairing computation in the ground field in
characteristic 3. Further, we intend to propose an integrated algorithm, which can compute
pairing in both cases. Finally, we will prove the correctness and analysis the performance for
this algorithm.
In the second subject, we will evaluate the pairing computation overhead for the
cryptographic application in wireless network for the devices under the restriction of
computation-limited, and design an appropriate pairing computation method by the
achievement of our first subject. |
| Appears in Collections: | [行動商務與多媒體應用學系] 科技部研究計畫
|
All items in ASIAIR are protected by copyright, with all rights reserved.
|
