Efficient Isogeny Computations on Twisted Edwards Curves
نویسندگان
چکیده
منابع مشابه
Twisted Edwards Curves Revisited
This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses 8M for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature ...
متن کاملTwisted Edwards Curves
This paper introduces “twisted Edwards curves,” a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents fast explicit formulas for twisted Edwards curves in projective and inverted coordinates; and sh...
متن کاملOn isogeny classes of Edwards curves over finite fields
We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a complete Edwards curve, and that an Edwards curve is isogenous to an original Edwards curve over IFq if and only if its group order is divisible by 8 if q ≡ −1 (mod 4), and 16 if q ≡ 1 (mod 4). Furthermore, ...
متن کاملMean value formulas for twisted Edwards curves
R. Feng, and H. Wu recently established a certain mean-value formula for the x-coordinates of the n-division points on an elliptic curve given in Weierstrass form (A mean value formula for elliptic curves, 2010, available at http://eprint.iacr.org/2009/586.pdf ). We prove a similar result for both the x and y-coordinates on a twisted Edwards elliptic curve.
متن کاملDivision Polynomials for Twisted Edwards Curves
This paper presents division polynomials for twisted Edwards curves. Their chief property is that they characterise the n-torsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these polynomials, which may aid computation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Security and Communication Networks
سال: 2018
ISSN: 1939-0114,1939-0122
DOI: 10.1155/2018/5747642