A complete set of addition laws for incomplete Edwards curves
نویسندگان
چکیده
منابع مشابه
A complete set of addition laws for incomplete Edwards curves
Edwards curves were the first curves shown to have a complete addition law. However, the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes incomplete over a quadratic field extension. This paper covers arbitrary Edwards curves and gives a set of two addition laws that for any pair of input points P1, P2 produce the sum P1 + P2.
متن کاملDifferential Addition on Edwards Curves
We give two parametrizations of points on Edwards curves that omit the X coordinate. The first parametrization leads to a differential addition formula that has the cost 5M + 4S, a doubling formula that has the cost 5S and a tripling formula that costs 4M+7S. The second one yields a differential addition formula with cost 5M + 2S and a doubling formula with cost 5S both even on generalized Edwa...
متن کاملEdwards curves and CM curves
Edwards curves are a particular form of elliptic curves that admit a fast, unified and complete addition law. Relations between Edwards curves and Montgomery curves have already been described. Our work takes the view of parameterizing elliptic curves given by their j-invariant, a problematic that arises from using curves with complex multiplication, for instance. We add to the catalogue the li...
متن کاملComplete Addition Formulas for Prime Order Elliptic Curves
An elliptic curve addition law is said to be complete if it correctly computes the sum of any two points in the elliptic curve group. One of the main reasons for the increased popularity of Edwards curves in the ECC community is that they can allow a complete group law that is also relatively efficient (e.g., when compared to all known addition laws on Edwards curves). Such complete addition fo...
متن کاملBinary Edwards Curves
This paper presents a new shape for ordinary elliptic curves over fields of characteristic 2. Using the new shape, this paper presents the first complete addition formulas for binary elliptic curves, i.e., addition formulas that work for all pairs of input points, with no exceptional cases. If n ≥ 3 then the complete curves cover all isomorphism classes of ordinary elliptic curves over F2n . Th...
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: Journal of Number Theory
سال: 2011
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2010.06.015