• Corpus ID: 18295068

Tutorial of Twisted Edwards Curves in Elliptic Curve Cryptography

  title={Tutorial of Twisted Edwards Curves in Elliptic Curve Cryptography},
  author={Emilie Menard Barnard},
  • 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… 
1 Citations
Efficient FPGA Implementation of Unified Point Operation for Twisted Edward Curve Cryptography
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.


Twisted Edwards Curves
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Twisted Edwards Curves Revisited
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Elliptic curve with Optimal mixed Montgomery-Edwards model for low-end devices
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
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A brief discussion on selecting new elliptic curves
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A normal form for elliptic curves
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Edwards Curves and Gaussian Hypergeometric Series
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University of California
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Twisted Edwards Curves.”Cryptology EPrint Archive
  • 2008