Construction of Rational Points on Elliptic Curves over Finite Fields

@inproceedings{Shallue2006ConstructionOR,
  title={Construction of Rational Points on Elliptic Curves over Finite Fields},
  author={Andrew Shallue and C. V. D. Woestijne},
  booktitle={ANTS},
  year={2006}
}
We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the curve. For this, we reduce the problem to the task of finding a rational point on a curve of genus zero. 
82 Citations
On hashing into elliptic curves
How to Hash into Elliptic Curves
  • T. Icart
  • Mathematics, Computer Science
  • IACR Cryptol. ePrint Arch.
  • 2009
Elligator Squared: Uniform Points on Elliptic Curves of Prime Order as Uniform Random Strings
Hashing into Hessian curves
Deterministic equation solving over finite fields
A note on the calculation of some functions in finite fields: Tricks of the Trade
  • M. Scott
  • Computer Science
  • IACR Cryptol. ePrint Arch.
  • 2020
Encoding Points on Hyperelliptic Curves over Finite Fields in Deterministic Polynomial Time
An Encoding for the Theta Model of Elliptic Curves
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 25 REFERENCES
Proper parametrization of surfaces with a rational pencil
Deterministic equation solving over finite fields
A course in computational algebraic number theory
  • H. Cohen
  • Computer Science, Mathematics
  • Graduate texts in mathematics
  • 1993
Algorithmic Number Theory
  • W. Bosma
  • Computer Science
  • Lecture Notes in Computer Science
  • 2000
Algebraic coding theory
  • E. Berlekamp
  • Computer Science
  • McGraw-Hill series in systems science
  • 1968
Sums of Four Squares
Graduate Texts in Mathematics
Basic Algebraic Geometry
Chapters 4–7
...
1
2
3
...