New Scalar Encoding Method to Accelerate Point Multiplication in Elliptic Curve Cryptography
The security of the wireless environment, especially for those which have limited resources like in the wireless sensor network, needs lightweight algorithms. Elliptic curve cryptography (ECC) is the unique algorithm which satisfies such property. It prov
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New Scalar Encoding Method to Accelerate Point Multiplication in Elliptic Curve Cryptography Chalak Shakir Ahmed, Min Jia, and Xuemai Gu
Abstract The security of the wireless environment, especially for those which have limited resources like in the wireless sensor network, needs lightweight algorithms. Elliptic curve cryptography (ECC) is the unique algorithm which satisfies such property. It provides the high level of security with relatively small keys; therefore, it has been the core of many standards. The efficiency of ECC is depending mostly on the implementation of the scalar multiplication which is accomplished mainly by addition and doubling operations. In the add-double method, reducing the number of ones is considered the most likely way to diminish the total number of the entirety operations. In this chapter, we present the method for recoding this scalar such that decreasing the number of addition operations. We compared our method with the one’s complement recoding method, and the simulation results showed that our proposed method produces mostly a better encoding. Keywords Elliptic curve cryptography • Encoding • Scalar multiplication • Hamming weight • Wireless sensor network.
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Introduction
Lately, wireless sensor networks (WSNs) have been widely used in pervading applications such as monitoring, detection and control applications. Security’s issues are mandatory due to the unreliable behaviour in wireless communications, which almost make the packets to be downfallen [1, 2]. Symmetric key schemes generally require sophisticated key management, which leads to a large memory and communication overhead. In contrast, public key based schemes have C.S. Ahmed (*) • M. Jia • X. Gu (*) School of Electronics and Information Technology, Harbin Institute of Technology HIT, Heilongjiang, Harbin 150001, China e-mail: [email protected]; [email protected]; [email protected]; [email protected] Q. Liang et al. (eds.), Communications, Signal Processing, and Systems, Lecture Notes in Electrical Engineering 202, DOI 10.1007/978-1-4614-5803-6_10, # Springer Science+Business Media New York 2012
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straightforward key management, but more computation time is needed [3]. In this chapter, we concentrate on the fold of encoding method for scalar k in Scalar Multiplication (SM), kP, where k is the scalar (key) and P is the point in the EC, and delicately overwhelming the complexity of ECC. Our method is used to represent the scalar k into a new form in the binary system. It used to decrease the hamming weight (non-zero elements “number of ones in the binary form”) of k , thereby, decreasing the number of addition operation, and as a result the calculations of SM is decreased. Nowadays, the direction of studies in the field of securing such miniature devices, as in wireless sensor networks, is focusing on the use of ECC with some considerations. Minimizing its computations is one of the most crucial attributes. Katti [4] proposed a new method for accelerating SM by depending on the
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