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for optimal tate pairing check on the elliptic curve alt_bn128, 2017. . [20] J. Camenisch and M. Stadler. Proof systems for general statements about discrete logarithms. Technical report, Dept. of Computer Science, ETH Zurich., 1997. [21] Jan Camenisch, Rafik Chaabouni, and abhi shelat. Efficient protocols for set membership and range proofs. In Josef Pieprzyk, editor, Advances in Cryptology - ASIACRYPT 2008 , pages 234–252. Springer, 2008. [22] Sébastien Canard, Iwen Coisel, Amandine Jambert, and Jacques Traoré. New results