Discrete mathematics forms the foundation for various fields, including computer science and cryptography, by providing essential tools for problem-solving in discrete structures. This paper explores the advancements in discrete mathematics, focusing on combinatorics and cryptography. It discusses the basic concepts of combinatorics, such as permutations, combinations, and graph theory, along with their applications in modern cryptography. The paper also examines symmetric and public key cryptography algorithms, including DES, AES, RSA, and ECC, highlighting their key features and security mechanisms. Furthermore, it explores the role of discrete structures, such as sets, relations, functions, and lattices, in cryptography, emphasizing their importance in designing secure cryptographic systems. Overall, this paper provides a comprehensive overview of the advancements in discrete mathematics and their applications in modern cryptography.