A new normal form x2 + y2 = c2(1 + x2y2) of elliptic curves was introduced by M. Harold
Edwards in 2007 over the field k having characteristic different than 2. This new form has
very special and important properties such that addition operation is strongly unified and
complete for properly chosen parameter c . In other words, doubling can be done by using
the addition formula and any two points on the curve can be added by the addition formula
without exception. D. Bernstein and T. Lange added one more parameter d to the normal
form to cover a large class of elliptic curves, x2 + y2 = c2(1 + dx2y2) over the same field.
In this thesis, an expository overview of the literature on Edwards curves is given. First, the
types of Edwards curves over the nonbinary field k are introduced, addition and doubling over
the curves are derived and efficient algorithms for addition and doubling are stated with their
costs. Finally, known elliptic curves and Edwards curves are compared according to their
cryptographic applications. The way to choose the Edwards curve which is most appropriate
for cryptographic applications is also explained.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12611065/index.pdf |
| Date | 01 September 2009 |
| Creators | Mus, Koksal |
| Contributors | Arslan, Sefa Feza |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | M.S. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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