Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards Curves

Autor:	Robert Dryło, Tomasz Kijko
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	twisted edwards curves complete set of addition formulas gröbner bases Electrical engineering. Electronics. Nuclear engineering TK1-9971 Telecommunication TK5101-6720
Zdroj:	International Journal of Electronics and Telecommunications, Vol vol. 66, Iss No 3, Pp 459-464 (2020)
Druh dokumentu:	article
ISSN:	2081-8491 2300-1933
DOI:	10.24425/ijet.2020.131899
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/6b6b4a0a8f7f402bbb94ff04ee52676a Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF