Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10

Non-supersingular curves are useful to improve the security of pairing-based cryptosystems. The method proposed by Brezing and Weng is computational inexpensive which can build suitable non-supersingular elliptic curves for pairing-based cryptosystems when the embedding degree is larger than 6. In this paper we propose a new method which extends Brezing and Weng’s method to generate more non-supersingular elliptic curves suitable for pairing-based cryptosystems. Furthermore, we show how our proposed method can be used in the method proposed by Scott and Barreto. Some examples are given to show that new non-supersingular curves can be built.

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