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FourQ: four-dimensional decompositions on a Q-curve over the Mersenne prime
four-dimensional decompositions Mersenne prime
2015/12/29
We introduce FourQ, a high-security, high-performance elliptic curve that targets the 128-
bit security level. At the highest arithmetic level, cryptographic scalar multiplications on FourQ can use
...
Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians
Elliptic curve cryptography number theory
2014/3/6
The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions using efficient endomorphisms---including Gallant--Lambert--Vanstone (GLV) and Galbraith--Lin--Scott (G...
Efficient Scalar Multiplication by Isogeny Decompositions
Elliptic curve cryptography fast arithmetic efficiently computable isogenies
2009/3/17
On an elliptic curve, the degree of an isogeny corresponds essentially
to the degrees of the polynomial expressions involved in its application.
The multiplicationby` map [`] has degree `2, theref...