Internet of Things (IoT) systems have experienced tremendous growth in all spheres of life that require a high level of security like smart cities, health, industrial automation, and smart transportation, which has resulted in a swelling of the cybersecurity threat spectrum. IoT environments may not be well covered by traditional security mechanisms because the devices are heterogeneous, have a small amount of computational resources, and are deployed in large scale and distributed. The literature review and risk management analysis of cryptographic and discrete approaches to cybersecurity of IoT is presented in this paper. The research methodologically analyzes lightweight cryptographic primitives, key administration protocols, authentication protocols as well as secure communication mechanisms specific to resource-constrained IoT devices. Simultaneously, discrete methods, such as graph theory, discrete event modeling, finite state machines, and combinatorial optimization, are discussed in terms of their usefulness in modeling attack surfaces, intrusion detection, trust management, and security policy enforcement. The paper also examines the IoT cyber risks by geographically mapping the various threats identified against the vulnerabilities and security controls using the current solutions, which reveals gaps between the identified vulnerabilities and the current solutions. According to the review, a formal risk management framework is addressed to facilitate a secure design of an IoT system, mitigate threats, and make decisions. The results highlight that the combination of cryptographic security and discrete modeling approaches can be used to increase resilience, scalability, and flexibility to changing cyber threats. The article is an informative resource to the researcher and practitioners interested in developing effective and resilient security solutions of next-generation IoT systems.