Many stream ciphers employ linear feedback shift registers (LFSRs) to generate pseudorandom sequences. Many recent LFSRs are defined in $GF\left(2^n\right)$ to take advantage of the n-bit processors, instead of using the classic binary field. In this way, the bit generation rate increases at the expense of a higher complexity in computations. For this reason, only certain primitive polynomials in $GF\left(2^n\right)$ are used as feedback polynomials in real ciphers. In this article, we present an efficient implementation of the LFSRs defined in $GF\left(2^n\right)$. The efficiency is achieved by using equivalent binary LFSRs in combination with binary n-bit grouped operations, n being the processor word’s length. This improvement affects the general considerations about the security of cryptographic systems that uses LFSR. The model also allows the development of a faster method to test the primitiveness of polynomials in $GF\left(2^n\right)$.

Well-known international security frameworks try to eliminate or mitigate different kinds of risks on the assets covered by their scopes (e.g., people, goods, information, and reputation). To date, to the best of our knowledge, any of these approaches neither provide a comprehensive perspective on security (considered as the merge of physical and logical security) nor consider sustainability as one of the levers for their design, implementation, and execution. This work presents a comprehensive security proposal through a framework that fits to the organizational security needs and contributes to the achievement of the sustainability objectives of an organization by avoiding duplicities and large security gaps from disjointed approaches. The work is supported by a methodology, which is the result of the wide and long work experience of the co-authors on security over the years in different organizations, businesses, and scopes. As it is shown in the theoretical exemplification included in the paper, the proposed framework combines the complementary and joint action of various actors for the protection of assets capable of achieving efforts and dedication efficiency, by merging the aspects of physical and logical security.