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Advanced Elliptic Curve Lecture

📝 Overview

This lecture covers two primary topics (see lecture.pdf):

  • Optimizing operations on elliptic curve: making ecadd and ecmul effective using projective coordinates.
  • Elliptic Curve pairings: properties, BLS signature, meaning of inputs and output.

📰 Content

File Description
lecture.pdf Lecture slides.
presentation.tex LaTeX source file.
ecpairing.sage SageMath code for elliptic curve pairings.
3d_ec_demo.nb Mathematica notebook for 3D elliptic curve visualization.

📚 Additional Resources

  • Craig Costello. "Pairings for Beginners": source.
  • Hankerson, Darrel, Scott A. Vanstone and Alfred Menezes. “Guide to Elliptic Curve Cryptography.” Springer Professional Computing (2004). source.
  • Beuchat, Jean-Luc & González-Díaz, Jorge & Mitsunari, Shigeo & Okamoto, Eiji & Rodríguez-Henríquez, Francisco & Teruya, Tadanori. (2010). "High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves". IACR Cryptology ePrint Archive. 2010. 21-39. 10.1007/978-3-642-17455-1_2. Preprint.