- Tytuł:
- Arithmetic Using Compression on Elliptic Curves in Huff’s Form and Its Applications
- Autorzy:
-
Dryło, Robert
Kijko, Tomasz
Wroński, Michał - Powiązania:
- https://bibliotekanauki.pl/articles/1844692.pdf
- Data publikacji:
- 2021
- Wydawca:
- Polska Akademia Nauk. Czytelnia Czasopism PAN
- Tematy:
-
Huff's curves
isogeny-based cryptography
compression functions on elliptic curves - Opis:
- In this paper for elliptic curves provided by Huff’s equation H a,b : ax(y² − 1) = by(x² − 1) and general Huff’s equation G a,b : x(ay² − 1) = y(bx² − 1) and degree 2 compression function f(x, y) = xy on these curves, herein we provide formulas for doubling and differential addition after compression, which for Huff’s curves are as efficient as Montgomery’s formulas for Montgomery’s curves By² = x³ + Ax² + x. For these curves we also provided point recovery formulas after compression, which for a point P on these curves allows to compute [n]f(P) after compression using the Montgomery ladder algorithm, and then recover [n]P. Using formulas of Moody and Shumow for computing odd degree isogenies on general Huff’s curves, we have also provide formulas for computing odd degree isogenies after compression for these curves. Moreover, it is shown herein how to apply obtained formulas using compression to the ECM algorithm.
- Źródło:
-
International Journal of Electronics and Telecommunications; 2021, 67, 2; 193-200
2300-1933 - Pojawia się w:
- International Journal of Electronics and Telecommunications
- Dostawca treści:
- Biblioteka Nauki
Artykuł