無線感測網路下適用於橢圓曲線加密機制之快速窗口純量乘法演算法

Abstract

最近幾年來，由於無線感測網路廣泛的應用在軍事、環境監控、健康和居家照顧上，使得其在安全性方面變得越來越重要。加密機制是一個提供安全服務的基本技術。因為感測節點的資源有限，所以在執行加密時必須減少計算、通信和記憶體的負載。橢圓曲線加密機制和其他的加密機制比較，其在通訊、計算和記憶體的使用需求上比較少。此外，在相同的安全層次上，橢圓曲線加密機制只需要160位元的金鑰長度，而RSA加密演算法則需要1024位元的金鑰長度，所以橢圓曲線加密機制非常適合用在無線感測網路上。然而，橢圓曲線加密機制的金鑰產生包含許多的純量乘法，使得其應用在感測節點上仍需要耗費許多的執行時間。在本論文中，我們提出一個在無線感測網路下適用於橢圓曲線加密機制之快速窗口純量乘法演算法(EW-MOF)。這個方法結合了相互交替型式和改良式窗口方法，它不只可以減少預先計算的時間和記憶體的使用，而且還可以減少每一個感測節點j。我們的分析結果顯示，EW-MOF所需要預先計算點的數目比1的補數演算法還要少，因此它非常適合用在無線感測網路上。此外，模擬結果顯示，我們提出的EW-MOF在不同的質數域下，包含預先計算時間的橢圓曲線加密機制，其平均金鑰產生時間比傳統1的補數演算法還要快24.69%。總之，在節省能源和金鑰產生時間方面，EW-MOF比1的補數演算法更適用在無線感測網路上。

In recent years, the security of wireless sensor networks (WSNs) has become more and more important due to extensive applications of WSNs in the areas of military, environmental monitoring, health and homecare. Cryptography is a basic technique to provide security services for WSNs. Owing to the limitation of resources in sensor nodes, the computation, communication, and memory overheads introduced by performing cryptography must be minimized. Elliptic curve cryptography (ECC) compared to other cryptosystems requires less communication, computation, and memory usages. Hence, ECC is suitable for wireless sensor network security because ECC only requires 160 bits length of keys to achieve the same level of security as RSA using 1024 bits length of keys. However, the key generations in ECC, which involve with a large number of scalar multiplications, is still time consuming when applied to sensor nodes. In this paper, we propose an enhanced window-based mutual opposite form (EW-MOF) for scalar multiplication with ECC in WSNs. The proposed EW-MOF combines MOF with an enhanced window method that can reduce not only pre-computation time and memory usage, but also average key generation time including pre-computation time in each sensor node. Our analysis has shown that the proposed EW-MOF requires a smaller number of essential pre-computed points than the one’s complement and therefore it is very suitable for WSNs. Simulation results show that the proposed EW-MOF is 24.69% faster than the one’s complement method, which is a classical method, in the average key generation time of ECC including pre-computation time under different field sizes. In summary, the proposed EW-MOF is more feasible than the one’s complement for wireless sensor networks in terms of key generation time and power saving.