  Castryck, Decru, and Smith used superspecial genus-2 curves and their
Richelot isogeny graph for basing genus-2 isogeny cryptography, and recently,
Costello and Smith devised an improved isogeny path-finding algorithm in the
genus-2 setting. In order to establish a firm ground for the cryptographic
construction and analysis, we give a new characterization of {\em decomposed
Richelot isogenies} in terms of {\em involutive reduced automorphisms} of
genus-2 curves over a finite field, and explicitly count such decomposed (and
non-decomposed) Richelot isogenies between {\em superspecial} principally
polarized abelian surfaces. As a corollary, we give another algebraic geometric
proof of Theorem 2 in the paper of Castryck et al.
