Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A One Round Protocol for Tripartite Diffie–Hellman
Journal of Cryptology
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
IEEE Transactions on Information Theory
Ordinary abelian varieties having small embedding degree
Finite Fields and Their Applications
Generating Pairing-Friendly Curves with the CM Equation of Degree 1
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Faster pairing computations on curves with high-degree twists
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
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The problem of constructing pairing-friendly elliptic curves has received a lot of attention. To find a suitable field for the construction we propose a method to find a polynomial u(x), by the method of indeterminate coefficients, such that 茂戮驴k(u(x)) factors. We also refine the algorithm by Brezing and Weng using a factor of 茂戮驴k(u(x)). As a result, we produce new families of parameters using our algorithm for pairing-friendly elliptic curves with embedding degree 8, and we compute some explicit curves as numerical examples.