• Corpus ID: 18295068

Tutorial of Twisted Edwards Curves in Elliptic Curve Cryptography

@inproceedings{Barnard2015TutorialOT,
  title={Tutorial of Twisted Edwards Curves in Elliptic Curve Cryptography},
  author={Emilie Menard Barnard},
  year={2015}
}
  • E. Barnard
  • Published 2015
  • Mathematics, Computer Science
This is a tutorial of Twisted Edwards curves. I plan to introduce them in comparison to Edwards curves, and review standard group law operations. I will then relate Twisted Edwards curves and Montgomery curves. I will also introduce a projective and other popular coordinate systems for Twisted Edwards curves. In addition, I will compare and contrast Twisted Edwards curves with Edwards curves, and briefly discuss the EdDSA application of Twisted Edwards curves. Lastly, I will present the latest… 
cs.ucsb.edu
1 Citations

One Citation

Citation Type

Citation Type

Efficient FPGA Implementation of Unified Point Operation for Twisted Edward Curve Cryptography
TLDR
A novel architecture of unified point operation has been designed over the 256-bit prime field which can execute Edward curve point doubling and point addition in one module instead of two divide modules and provides better performance in terms of throughput on FPGA than the other work.

References

SHOWING 1-10 OF 20 REFERENCES
Twisted Edwards Curves
This paper introduces "twisted Edwards curves," a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular…
Twisted Edwards Curves Revisited
TLDR
The new point addition algorithm can be used to provide a natural protection from side channel attacks based on simple power analysis (SPA) and allow faster implementation of elliptic curve scalar multiplication.
Elliptic curve with Optimal mixed Montgomery-Edwards model for low-end devices
TLDR
The implementation, performed in constant-time, reduces the execution time by up to 14% and 18% for fixed point and random point scalar multiplication, respectively, when comparing with the state-of-the-art implementation on the identical platform.
Edwards Curves
  • T. Lange
  • Mathematics
    Encyclopedia of Cryptography and Security
  • 2011
Twisted Hessian Curves
This paper presents new speed records for arithmetic on a large family of elliptic curves with cofactor 3: specifically, 8.77Mper bit for 256-bit variable-base single-scalar multiplication when curve…
A brief discussion on selecting new elliptic curves
This position paper summarizes our perspectives on the selection of next-generation elliptic curves for standardization. It also contains generation algorithms intended as a foundation for choosing…
A normal form for elliptic curves
The normal form x2+y2 = a2+a2x2y2 for elliptic curves simplifies formulas in the theory of elliptic curves and functions. Its principal advantage is that it allows the addition law, the group law on…
Edwards Curves and Gaussian Hypergeometric Series
TLDR
The number of rational points of E is expressed using the Gaussian hypergeometric series and the existence of isogenies between E and Legendre elliptic curves over $\mathbb{F}_p$ is proved.
University of California
TLDR
The above physicians are investigating a method of treating metastatic pheochromocytoma with a radioactive compound called 131 I-metaiodobenzylguanidine (131 I-MIBG), which delivers the radioactive iodine to the cancer cells selectively, resulting in their destruction.
Twisted Edwards Curves.”Cryptology EPrint Archive
  • 2008
...
1
2
...