Elliptic Curves, Group Law, and Efficient Computation

I will demonstrate techniques to derive the addition law on an arbitrary elliptic curve. The derived addition laws are applied to provide methods for efficiently adding points. The contributions immediately find applications in cryptology such as the efficiency improvements for elliptic curve scalar multiplication and cryptographic pairing computations. In particular, contributions are made to case of the following five forms of elliptic curves:

  1. Short Weierstrass form, y2 = x3 + ax + b,
  2. Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1,
  3. Twisted Hessian form, ax3 + y3 + 1 = dxy,
  4. Twisted Edwards form, ax2 + y2 = 1 + dx2y2,
  5. Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1.

These forms are the most promising candidates for efficient computations and thus considered in this talk. Nevertheless, the employed methods are capable of handling arbitrary elliptic curves.

Speaker Details

Ed Dawson is an Emeritus Professor in the Information Security Institute (ISI) at Queensland University of Technology in Brisbane Australia. Prior to this Professor Dawson was Research Director of the ISI. He has extensive experience in research in cryptology over the past 24 years with over 250 research papers and supervising 25 PhD students to completion. He has lead various applied research projects dealing with different aspects of information security. Currently he is serving as the Vice President of the International Association of Cryptologic Research (IACR).

Date:
Speakers:
Ed Dawson
Affiliation:
Queensland University of Technology

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