# New Scalar Encoding Method to Accelerate Point Multiplication in Elliptic Curve Cryptography

## 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.## Notes

### Acknowledgments

This work is supported by National Science and Technology Major Project of the Ministry of Science and Technology of China (2010ZX03006-002-02), the National Natural Science Foundation of China (Grant No. 61201143), the National Science Foundation for Post-doctoral Scientists of China (Grant No. 2012M510956), the Post-doctoral Funds of Heilongjiang Province (Grant No.LBHZ11128), and the Fundamental Research Funds for the Central Universities (Grant No. HIT. NSRIF. 2010091).

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