We explore the connections between two fields of study—the algorithmic foundations and the domains of information security and privacy. The principles of algorithmic foundations are instrumental in enhancing the efficiency of cryptographic systems. This is particularly relevant for post-quantum cryptography systems like isogeny-based cryptography, which benefit from efficient implementations. Conversely, methods from information privacy can be applied to ensure the trustability of several combinatorial algorithms, including linear integer programming and triangle counting. In this chapter, we delve into the role of algorithms capable of determining a lower bound for the set-k-multicover problem in ensuring the security of homomorphic secret sharing systems. Homomorphic secret sharing is a scheme that enables the delegation of computational tasks to servers while maintaining the confidentiality of our data. Within this framework, servers are tasked with producing a computational outcome based on the secrets of clients, without gaining any knowledge about the clients themselves. We posit that the maximum number of clients that this system can accommodate is directly linked to the optimal value of the set-k-multicover problem. Consequently, to calculate the upper limit of clients that the system can feasibly support, we introduce an algorithm aimed at identifying a lower bound for the optimal solution of this problem.