The Continued Fraction Algorithm and Regulator for Quadratic Function Fields of Characteristic 2 Original Research Article

The continued fraction expansion and infrastructure for quadratic congruence function fields of odd characteristic have been well studied. Recently, these ideas have even been used to produce cryptosystems. Much less is known concerning the continued fraction expansion and infrastructure for quadratic function fields of even characteristic. We will explore these ideas, and show that the situation is very similar to the odd characteristic case. This exploration will result in a method for computing the regulator for quadratic function fields of characteristic 2.