Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards Curves
Daniel Bernstein and Tanja Lange [9] proved that two given addition formulas on twisted Edwards elliptic curves ax2 +y2 = 1+dxy are complete (i.e. the sum of any two points on a curve can be computed using one of these formulas). In this paper we give simple verification of completeness of these for...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2020-09-01
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| Series: | International Journal of Electronics and Telecommunications |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/115226/PDF/63_2571_Dry%C5%82o_L_skl.pdf |
| _version_ | 1811343556212686848 |
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| author | Robert Dryło Tomasz Kijko |
| author_facet | Robert Dryło Tomasz Kijko |
| author_sort | Robert Dryło |
| collection | DOAJ |
| description | Daniel Bernstein and Tanja Lange [9] proved that two given addition formulas on twisted Edwards elliptic curves ax2 +y2 = 1+dxy are complete (i.e. the sum of any two points on a curve can be computed using one of these formulas). In this paper we give simple verification of completeness of these formulas using a program written in Magma, which is based on the fact that completeness means that some systems of polynomial equations have no solutions. This method may also be useful to verify completeness of additions formulas on other models of elliptic curves. |
| first_indexed | 2024-04-13T19:32:23Z |
| format | Article |
| id | doaj.art-6b6b4a0a8f7f402bbb94ff04ee52676a |
| institution | Directory Open Access Journal |
| issn | 2081-8491 2300-1933 |
| language | English |
| last_indexed | 2024-04-13T19:32:23Z |
| publishDate | 2020-09-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | International Journal of Electronics and Telecommunications |
| spelling | doaj.art-6b6b4a0a8f7f402bbb94ff04ee52676a2022-12-22T02:33:09ZengPolish Academy of SciencesInternational Journal of Electronics and Telecommunications2081-84912300-19332020-09-01vol. 66No 3459464https://doi.org/10.24425/ijet.2020.131899Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards CurvesRobert DryłoTomasz KijkoDaniel Bernstein and Tanja Lange [9] proved that two given addition formulas on twisted Edwards elliptic curves ax2 +y2 = 1+dxy are complete (i.e. the sum of any two points on a curve can be computed using one of these formulas). In this paper we give simple verification of completeness of these formulas using a program written in Magma, which is based on the fact that completeness means that some systems of polynomial equations have no solutions. This method may also be useful to verify completeness of additions formulas on other models of elliptic curves.https://journals.pan.pl/Content/115226/PDF/63_2571_Dry%C5%82o_L_skl.pdftwisted edwards curvescomplete set of addition formulasgröbner bases |
| spellingShingle | Robert Dryło Tomasz Kijko Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards Curves International Journal of Electronics and Telecommunications twisted edwards curves complete set of addition formulas gröbner bases |
| title | Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards Curves |
| title_full | Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards Curves |
| title_fullStr | Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards Curves |
| title_full_unstemmed | Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards Curves |
| title_short | Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards Curves |
| title_sort | simple verification of completeness of two addition formulas on twisted edwards curves |
| topic | twisted edwards curves complete set of addition formulas gröbner bases |
| url | https://journals.pan.pl/Content/115226/PDF/63_2571_Dry%C5%82o_L_skl.pdf |
| work_keys_str_mv | AT robertdryło simpleverificationofcompletenessoftwoadditionformulasontwistededwardscurves AT tomaszkijko simpleverificationofcompletenessoftwoadditionformulasontwistededwardscurves |