  In the two-part paper, we consider the problem of secure network coding when
the information rate and the security level can change over time. To
efficiently solve this problem, we put forward local-encoding-preserving secure
network coding, where a family of secure linear network codes (SLNCs) is called
local-encoding-preserving (LEP) if all the SLNCs in this family share a common
local encoding kernel at each intermediate node in the network. In this paper
(Part II), we first consider the design of a family of LEP SLNCs for a fixed
rate and a flexible security level. We present a novel and efficient approach
for constructing upon an SLNC that exists an LEP SLNC with the same rate and
the security level increased by one. Next, we consider the design of a family
of LEP SLNCs for a fixed dimension (equal to the sum of rate and security
level) and a flexible pair of rate and security level. We propose another novel
approach for designing an SLNC such that the same SLNC can be applied for all
the rate and security-level pairs with the fixed dimension. Also, two
polynomial-time algorithms are developed for efficient implementations of our
two approaches, respectively. Furthermore, we prove that both approaches do not
incur any penalty on the required field size for the existence of SLNCs in
terms of the best known lower bound by Guang and Yeung. Finally, we consider
the ultimate problem of designing a family of LEP SLNCs that can be applied to
all possible pairs of rate and security level. By combining the construction of
a family of LEP SLNCs for a fixed security level and a flexible rate (obtained
in Part I) with the constructions of the two families of LEP SLNCs in the
current paper in suitable ways, we can obtain a family of LEP SLNCs that can be
applied for all possible pairs of rate and security level. Three possible such
constructions are presented.
