Improvements in the computation of the Hasse-Witt matrix

Abstract

The Hasse-Witt matrix of a hyperelliptic curve gives partial information for the order of the Jacobian of the curve, therefore the Hasse-Witt matrices can be used for point counting of hyperelliptic curves. Bostan, Gaudry and Schost improved the Chudnovsky-Chudnovsky algorithm and computed the Hasse-Witt matrices by using their improved algorithm for constructing hyperelliptic cryptosystems. The both algorithms need $p$-adic integers with finite precision as the base operations. This paper shows improvements in the computation of the Hasse-Witt matrix that reduces the required precision of the $p$-adic integers.