A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
The Mathematica Book
A One Round Protocol for Tripartite Diffie–Hellman
Journal of Cryptology
Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems
Journal of Cryptology
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Faster addition and doubling on elliptic curves
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Efficient computation of tate pairing in projective coordinate over general characteristic fields
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Another Approach to Pairing Computation in Edwards Coordinates
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
Delaying mismatched field multiplications in pairing computations
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Another elliptic curve model for faster pairing computation
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
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
Avoiding full extension field arithmetic in pairing computations
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
Refinement of miller's algorithm over edwards curves
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
Fast tate pairing computation on twisted Jacobi intersections curves
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
Tate pairing computation on jacobi's elliptic curves
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
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A new form of elliptic curve was recently discovered by Edwards and their application to cryptography was developed by Bernstein and Lange. The form was later extended to the twisted Edwards form. For cryptographic applications, Bernstein and Lange pointed out several advantages of the Edwards form in comparison to the more well known Weierstraß form. We consider the problem of pairing computation over Edwards form curves. Using a birational equivalence between twisted Edwards and Weierstraß forms, we obtain a closed form expression for the Miller function computation.Simplification of this computation is considered for a class of supersingular curves. As part of this simplification, we obtain a distortion map similar to that obtained for Weierstraß form curves by Barreto et al and Galbraith et al. Finally, we present explicit formulae for combined doubling and Miller iteration and combined addition and Miller iteration using both inverted Edwards and projective Edwards coordinates. For the class of supersingular curves considered here, our pairing algorithm can be implemented without using any inversion.