Algorithmic number theory
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Elliptic curves in cryptography
Elliptic curves in cryptography
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
A One Round Protocol for Tripartite Diffie–Hellman
Journal of Cryptology
Short Signatures from the Weil Pairing
Journal of Cryptology
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Efficient computations of the Tate pairing for the large MOV degrees
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
On compressible pairings and their computation
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Faster pairings using an elliptic curve with an efficient endomorphism
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
CT-RSA'05 Proceedings of the 2005 international conference on Topics 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
IEEE Transactions on Information Theory
The tate pairing via elliptic nets
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Computing bilinear pairings on elliptic curves with automorphisms
Designs, Codes and 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
| Hi-index | 0.00 |
To reduce bandwidth in elliptic curve cryptography one can transmit only x-coordinates of points (or x-coordinates together with an extra bit). This is called point compression. For further computation using the points one can either recover the y-coordinates by taking square roots or one can use point multiplication formulae which use x-coordinates only. We consider how to efficiently use point compression in pairing-based cryptography when the embedding degree is even. We give a method to compute compressed pairings using x-coordinates only. We also show how to compute the compressed pairings using two x-coordinates and one y-coordinate. Our methods are more efficient than taking square roots when the embedding degree is small. We implemented the algorithms in the case of embedding degree 2 curves over $${\mathbb {F}_p}$$ where $${p \equiv 3}$$ (mod 4) and found that our methods can be 10---15% faster than the analogous methods using square roots.