id: 05853505
dt: j
an: 05853505
au: Duquesne, Sylvain
ti: Traces of the group law on the Kummer surface of a curve of genus 2 in
    characteristic 2.
so: Math. Comput. Sci. 3, No. 2, 173-183 (2010).
py: 2010
pu: Birkhäuser (Springer), Basel
la: EN
cc: 
ut: 
ci: Zbl 0857.14018
li: doi:10.1007/s11786-009-0013-x
ab: Summary: In the early 1990s, Flynn [cf. {\it J. W. S. Cassels} and {\it E.
    V. Flynn}, Prolegomena to a middlebrow arithmetic of curves of genus 2.
    (Cambridge Univ. Press) (1996; Zbl 0857.14018)] gave an explicit
    description of the Jacobian of a genus 2 hyperelliptic curve in order
    to perform efficient arithmetic on these objects. In this paper, we
    give a generalization of Flynn’s work when the ground field has
    characteristic 2. More precisely, we give an explicit description of
    the Kummer surface. We also give and explain how we found, using
    symbolic computations, explicit formulas for the structure of the group
    law on the Jacobian preserved on the Kummer surface. Finally, we use
    these new objects to give a very fast scalar multiplication algorithm
    for hyperelliptic curve cryptography in characteristic 2.
rv: