Advances in Applied Mathematics
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Pairing Computation on Twisted Edwards Form Elliptic Curves
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Another Approach to Pairing Computation in Edwards Coordinates
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
Jacobi Quartic Curves Revisited
ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
Faster Pairings on Special Weierstrass Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
The Jacobi model of an elliptic curve and side-channel analysis
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Faster group operations on elliptic curves
AISC '09 Proceedings of the Seventh Australasian Conference on Information Security - Volume 98
Twisted jacobi intersections curves
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems
IEEE Transactions on Information Theory
Reducing elliptic curve logarithms to logarithms in a finite field
IEEE Transactions on Information Theory
Ordinary abelian varieties having small embedding degree
Finite Fields and Their Applications
| Hi-index | 0.00 |
We propose for the first time the computation of the Tate pairing on Jacobi intersection curves. For this, we use the geometric interpretation of the group law and the quadratic twist of Jacobi intersection curves to obtain a doubling step formula which is efficient but not competitive compared to the case of Weierstrass curves, Edwards curves and Jacobi quartic curves. As a second contribution, we improve the doubling and addition steps in Miller's algorithm to compute the Tate pairing on the special Jacobi quartic elliptic curve Y2=dX4+Z4. We use the birational equivalence between Jacobi quartic curves and Weierstrass curves together with a specific point representation to obtain the best result to date among all the curves with quartic twists. In particular for the doubling step in Miller's algorithm, we obtain a theoretical gain between 6% and 21%, depending on the embedding degree and the extension field arithmetic, with respect to Weierstrass curves [6] and Jacobi quartic curves [23].