In this chapter, the advancements in Cellular Automata (CA) and their impact on the field of cryptography are discussed. While the role of CA in cryptography was initially limited to elementary CA, recent developments have shown that CA can be a valuable primitive to resist fault attacks and enhance the security of cryptographic systems. Traditionally, CA-based stream ciphers have been proposed and utilized in cryptography. These ciphers leverage the parallel nature of CA to achieve efficient and secure encryption of data. However, with the rapid growth of computing resources in today’s digital era, attackers have access to significant computational power which can be used to launch various types of attacks including side-channel attacks. As computing resources become more powerful, cryptographic algorithms that are considered secure today may become vulnerable in the near future. This necessitates the exploration of new approaches to strengthen information security. In recent years, there has been a growing focus on exploring cryptographically secure higher radii CA rules and their potential to enhance the security of cryptographic systems in today’s world. By investigating and utilizing higher radii CA rules, researchers aim to develop cryptographic algorithms that can withstand the increasing computational capabilities of attackers. These higher radii CA rules offer new possibilities for designing robust and secure cryptographic primitives that can resist various types of attacks including side-channel attacks. The exploration of cryptographically secure higher radii CA rules reflects the need to continually adapt cryptographic techniques to address emerging threats. By incorporating advancements in CA and other areas of cryptography, it is possible to develop more resilient and secure cryptographic algorithms that can withstand the challenges posed by advancing computing resources.