Studies on Tate Pairing Computations on Edwards Curves and a Strongly Unified Addition Formula for Elliptic Curves.

Date of Submission

December 2010

Date of Award

Winter 12-12-2011

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science


Theoretical Statistics and Mathematics Unit (TSMU-Bangalore)


Barua, Rana (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

This report is a study of elliptic curves, group law on elliptic curves, scalar multiplications and then we focused on pairing computations on elliptic curves. Elliptic curves has wide application in Cryptography. This reports presents addition formula on elliptic curves in various coordinates and concentrates primarily on the Tate pairings on Edwards curves.In this report, we propose a new addition formula on Weierstrass form elliptic curves in three coordinate systems namely, affine, Projective and Jacobian in chapter 2. The main advantage of our proposed addition algorithms is it is strongly unified. This means that the formulas work for all pairs of inputs except neutral element, simplifying protection against side-channel attacks. Then we extensively compute addition and doubling cost, compare with different forms of elliptic curves in different coordinate systems.The Bilinear map or Pairing like Weil pairing or Tate pairing on elliptic curves has played a vital role in designing various cryptographic schemes. I have studied Tate pairing computations on Edwards curves. In chapter 3 we have summarized different proposed method of finding Tate pairing on Edwards curves. I do not have any contribution in this area.Related Works: After we have obatined these formulas we noticed that Dier et. all [28] have obtained these earlier. However, such a detailed study was not carried out. Here, we provide much explicit results in three coordinates namely, affine, Projective, Jacobian. We also computed addition and doubling cost for each case and compared with usual addition rule.


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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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