Searching for authors named "Christophe Doche" – sorted by Relevance.
8 documents found, showing 1 through 8.
-
On the spectrum of the Zhang-Zagier height
- …Abstract. From recent work of Zhang and of Zagier, we know that their height H(α) is bounded away from 1 for every algebraic number α different from 0, 1, 1/2 ± √ −3/2. The study of the related spectrum is especially interesting, for it is linked to Lehmer’s problem and to a conjecture of Bogomolov…
- Cited by 3 (1 self) – Add To MetaCart
-
Redundant Trinomials for Finite Fields of Characteristic 2
- …In this paper we introduce so-called redundant trinomials to represent elements of nite elds of characteristic 2. The concept is in fact similar to almost irreducible trinomials introduced by Brent and Zimmermann in the context of random numbers generators in [BZ ####]. See also [BZ]. In fact, B…
- Cited by 4 (0 self) – Add To MetaCart
-
On the real roots of generalized Thue-Morse polynomials
- …this article we investigate real roots of real polynomials. By results of M. Kac [8, 9, 10] we know that a polynomial of degree n has in average 2…
- Cited by 1 (1 self) – Add To MetaCart
-
Extended double-base number system with applications to elliptic curve cryptography
- …Abstract. We investigate the impact of larger digit sets on the length of Double-Base Number system (DBNS) expansions. We present a new representation system called extended DBNS whose expansions can be extremely sparse. When compared with double-base chains, the average length of extended DBNS expa…
- Cited by 6 (1 self) – Add To MetaCart
-
Efficient scalar multiplication by isogeny decompositions
- …Abstract. On an elliptic curve, the degree of an isogeny corresponds essentially to the degrees of the polynomial expressions involved in its application. The multiplication–by–ℓ map [ℓ] has degree ℓ 2, therefore the complexity to directly evaluate [ℓ](P) isO(ℓ 2). For a small prime ℓ ( = 2,3) such …
- Cited by 9 (0 self) – Add To MetaCart
-
Extending scalar multiplication using double bases
- …Abstract. It has been recently acknowledged [4, 6, 9] that the use of double bases representations of scalars n, that is an expression of the form n = � e,s,t (−1)eA s B t can speed up significantly scalar multiplication on those elliptic curves where multiplication by one base (say B) is fast. This…
- Cited by 4 (4 self) – Add To MetaCart
-
Real Roots!
- ……
- Add To MetaCart
-
Integral Geometry and Real Zeros of Thue-Morse Polynomials
- …We study the average number of intersecting points of a given curve with random hyperplanes in an n-dimensional Euclidean space. As noticed by A. Edelman and E. Kostlan this problem is closely linked to nding the average number of real zeros of random polynomials. They show that a real polynomial of…
- Cited by 2 (2 self) – Add To MetaCart
Showing 1 through 8.
