International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Christophe Ritzenthaler

Publications

Year
Venue
Title
2006
ASIACRYPT
2006
EPRINT
Distortion maps for genus two curves
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
Fast addition on non-hyperelliptic genus $3$ curves
St?phane Flon Roger Oyono Christophe Ritzenthaler
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.