Algebra and combinatorics play crucial roles in the field of cryptography. Algebraic structures, such as groups, rings, and fields, form the foundation of many cryptographic algorithms. For example, the RSA encryption algorithm relies on properties of prime numbers and modular arithmetic, both of which are rooted in algebra. Elliptic curve cryptography (ECC) is another application that uses the algebraic structure of elliptic curves over finite fields to create efficient and secure cryptographic schemes. Combinatorics, the study of counting, arrangement, and combination, is essential for analyzing and designing cryptographic protocols. It helps in understanding the complexity and security of these protocols. For instance, combinatorial designs and permutations are used in the construction of block ciphers like the Data Encryption Standard (DES) and Advanced Encryption Standard (AES). The synergy of algebra and combinatorics provides robust tools for developing and analyzing cryptographic systems. In this talk, I will present several concrete examples to illustrate how the interplay between algebra and combinatorics enriches cryptography in the constructions of cryptographic schemes such as secret sharing and secure multiparty computation.