  Key establishment is the basic necessary tool in the network security, by
which pairs in the network can establish shared keys for protecting their
pairwise communications. There have been some key agreement or predistribution
schemes with the property that the key can be established without the
interaction (\cite{Blom84,BSHKY92,S97}). Recently the hierarchical cryptography
and the key management for hierarchical networks have been active topics(see
\cite{BBG05,GHKRRW08,GS02,HNZI02,HL02,Matt04}. ). Key agreement schemes for
hierarchical networks were presented in \cite{Matt04,GHKRRW08} which is based
on the Blom key predistribution scheme(Blom KPS, [1]) and pairing. In this
paper we introduce generalized Blom-Blundo et al key predistribution schemes.
These generalized Blom-Blundo et al key predistribution schemes have the same
security functionality as the Blom-Blundo et al KPS. However different and
random these KPSs can be used for various parts of the networks for enhancing
the resilience. We also presentkey predistribution schemes from a family
hyperelliptic curves. These key predistribution schemes from different random
curves can be used for various parts of hierarchical networks. Then the
non-interactive, identity-based and dynamic key predistributon scheme based on
this generalized Blom-Blundo et al KPSs and hyperelliptic curve KPSs for
hierarchical networks with the following properties are constructed.
1)$O(A_KU)$ storage at each node in the network where $U$ is the expansion
number and $A_K$ is the number of nodes at the $K$-th level of the hierarchical
network; 2)Strongly resilience to the compromising of arbitrary many leaf and
internal nodes; 3)Information theoretical security without random oracle.
