Elliptic curves in cryptography
Elliptic curves in cryptography
Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
On degrees of polynomial interpolations related to elliptic curve cryptography
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
A polynomial form for logarithms modulo a prime (Corresp.)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Polynomial approximation of bilinear Diffie--Hellman maps
Finite Fields and Their Applications
On the minimal embedding field
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
The Diffie---Hellman problem and generalization of Verheul's theorem
Designs, Codes and Cryptography
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Using the Miller algorithm, we can efficiently compute the Weil pairing for two given points on an elliptic curve. On the other hand, security of pairing based cryptographic protocols depends on the converse problem: find a point on an elliptic curve whose Weil pairing with a given (fixed) point is equal to a given root of unity, which we call the Weil pairing inversion problem. In this article, we give closed formulae which give a solution to the problem. For supersingular elliptic curves over fields of characteristic two or three, these formulae take more simpler forms than those for other elliptic curves.