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In the two-part paper, we consider the problem of secure network coding whenthe information rate and the security level can change over time. Toefficiently solve this problem, we put forward local-encoding-preserving securenetwork coding, where a family of secure linear network codes (SLNCs) is calledlocal-encoding-preserving (LEP) if all the SLNCs in this family share a commonlocal 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 fixedrate and a flexible security level. We present a novel and efficient approachfor constructing upon an SLNC that exists an LEP SLNC with the same rate andthe security level increased by one. Next, we consider the design of a familyof LEP SLNCs for a fixed dimension (equal to the sum of rate and securitylevel) and a flexible pair of rate and security level. We propose another novelapproach for designing an SLNC such that the same SLNC can be applied for allthe rate and security-level pairs with the fixed dimension. Also, twopolynomial-time algorithms are developed for efficient implementations of ourtwo approaches, respectively. Furthermore, we prove that both approaches do notincur any penalty on the required field size for the existence of SLNCs interms of the best known lower bound by Guang and Yeung. Finally, we considerthe ultimate problem of designing a family of LEP SLNCs that can be applied toall possible pairs of rate and security level. By combining the construction ofa family of LEP SLNCs for a fixed security level and a flexible rate (obtainedin Part I) with the constructions of the two families of LEP SLNCs in thecurrent paper in suitable ways, we can obtain a family of LEP SLNCs that can beapplied for all possible pairs of rate and security level. Three possible suchconstructions are presented.

Local-Encoding-Preserving Secure Network Coding---Part II: Flexible Rate and Security Level