Semistable models of elliptic curves over residue characteristic 2
نویسندگان
چکیده
منابع مشابه
Fast hashing onto elliptic curves over fields of characteristic 3
We describe a fast hash algorithm that maps arbitrary messages onto points of an elliptic curve defined over a finite field of characteristic 3. Our new scheme runs in time O(m) for curves over F3m . The best previous algorithm for this task runs in time O(m). Experimental data confirms the speedup by a factor O(m), or approximately a hundred times for practical m values. Our results apply for ...
متن کاملEfficient Arithmetic on Elliptic Curves over Fields of Characteristic Three
This paper presents new explicit formulae for the point doubling, tripling and addition for ordinary Weierstraß elliptic curves with a point of order 3 and their equivalent Hessian curves over finite fields of characteristic three. The cost of basic point operations is lower than that of all previously proposed ones. The new doubling, mixed addition and tripling formulae in projective coordinat...
متن کاملRoot Numbers of Semistable Elliptic Curves in Division Towers
The growth of the Mordell-Weil rank of an elliptic curve in a tower of number fields can be discussed at many levels. On the one hand, the issues raised can be embedded in a broader Iwasawa theory of elliptic curves (Mazur [10]); on the other hand, they can be crystallized in a single easily stated question, namely whether the rank of the elliptic curve over subextensions of finite degree is bo...
متن کاملPoint Multiplication on Supersingular Elliptic Curves Defined over Fields of Characteristic 2 and 3
Elliptic curve cryptosystem protocols use two main operations, the scalar multiplication and the pairing computation. Both of them are done through a chain of basic operation on the curve. In this paper we present new formulas for supersingular elliptic curve in characteristic 2 and 3. We improve best known formulas by at least one multiplication in the field.
متن کاملOn elliptic curves in characteristic 2 with wild additive reduction
Introduction. In [Ge1] Gekeler classified all elliptic curves over F2r (T ) with one rational place of multiplicative reduction (without loss of generality located at ∞), one further rational place of bad reduction (without loss of generality located at 0) and good reduction elsewhere. So these curves have conductor ∞ · T where n is a natural number (which actually can be arbitrarily large). In...
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: Canadian Mathematical Bulletin
سال: 2020
ISSN: 0008-4395,1496-4287
DOI: 10.4153/s0008439520000326