ZHANG Lijun, WANG Kunpeng, WANG Hong. Unified and Complete Point Addition Formula for Elliptic Curves[J]. Chinese Journal of Electronics, 2012, 21(2): 345-349.
Citation: ZHANG Lijun, WANG Kunpeng, WANG Hong. Unified and Complete Point Addition Formula for Elliptic Curves[J]. Chinese Journal of Electronics, 2012, 21(2): 345-349.

Unified and Complete Point Addition Formula for Elliptic Curves

  • Received Date: 2011-01-01
  • Rev Recd Date: 2011-07-01
  • Publish Date: 2012-04-25
  • As is well known, the unified point addition formula is useful for resisting side channel attacks in elliptic curve cryptography. Furthermore, if the unified formula is complete, which means it is valid for any two points, then there are no exceptional cases to be described particularly. This feature is especially preferable for elegant codes of elliptic crypto-algorithms. Therefore, the unified and also complete point addition formula can provide the advantage for good security and convenient implementation. In this paper, we exploit sufficient and necessary condition for the existence of unified and complete point addition formula on several known elliptic curve models such asWeierstrass cubics, Jacobi quartics, Edwards curves, etc.. Moreover, we study another form of elliptic curves called Selmer curves. For practical application, we finally give some numerical examples of cryptographic secure Selmer curves.
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      沈阳化工大学材料科学与工程学院 沈阳 110142

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