## CryptoDB

### Christophe Ritzenthaler

#### Publications

Year
Venue
Title
2006
ASIACRYPT
2006
EPRINT
Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus $g > 1$ is more complicated since the full torsion subgroup has rank $2g$. In this paper we prove that distortion maps always exist for supersingular curves of genus $g>1$ and we give several examples in genus $2$.
2004
EPRINT
We present a fast addition algorithm in the Jacobian of a genus $3$ non-hyperelliptic curve over a field of any characteristic. When the curve has a rational flex and $\textrm{char}(k) > 5$, the computational cost for addition is $148M+15SQ+2I$ and $165M+20SQ+2I$ for doubling. An appendix focuses on the computation of flexes in all characteristics. For large odd $q$, we also show that the set of rational points of a non-hyperelliptic curve of genus $3$ can not be an arc.

#### Coauthors

Stéphane Flon (1)
Steven D. Galbraith (1)
Pierrick Gaudry (1)
T. Houtmann (1)
David Kohel (1)
Roger Oyono (1)
Jordi Pujol\`as (1)
Benjamin Smith (1)
A. Weng (1)