The article features the technical development in the process of designing public-key cryptography to protect international commerce and communications. In 1997, the National Institute of Standards and Technology (NIST) announced a competition for the algorithm, Data Encryption Standard replacement, and held public meetings to discuss the criteria for a proposed Advanced Encryption Standard (AES) with much focus on its key length. NIST allowed foreign participation in the AES competition, settling requirements like implementation of symmetric key cryptography, must of an algorithm to be a block cipher, designing 128-bit blocks algorithm and to have three key sizes of 128, 192 and 256 bits. While designing, nonlinear functions form the basis of cryptographic design. Simplest techniques for encrypting a block of symbols are substitution, which replaces a symbol by another and transposition permutes the symbols of a block around. The purpose of a cryptosystem is to make decryption of messages extremely difficult without the key and the design of a cryptosystem has a dual objective, ensuring difficulty in cryptanalysis while enabling certification of the algorithm's security. Block-structured algorithms, whose non-linearity is achieved by substitution boxes attacked by differential and linear cryptanalysis.