Constructing Symmetric Pairings over Supersingular Elliptic Curves with Embedding Degree Three

In the present paper, we propose constructing symmetric pairings by applying the Ate pairing to supersingular elliptic curves over finite fields that have large characteristics with embedding degree three. We also propose an efficient algorithm of the Ate pairing on these curves. To construct the algorithm, we apply the denominator elimination technique and the signed-binary approach to the Miller's algorithm, and improve the final exponentiation. We then show the efficiency of the proposed method through an experimental implementation.

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