Wireless networks afford numerous benefits for productivity, due to the ease of access to information resources. A network can now be set up and changed more quickly, with less effort, and for less money. However, wireless technology also creates new threats; and alerts the existing risk profile for information security. In Wireless Fidelity (Wi-Fi), security mechanisms such as encryption algorithms play a vital role. A large amount of memory and power is consumed by those algorithms. This research study therefore proposed a Computation Efficient Secure Algorithm (CESA) that reduces the high consumption of power and memory to efficiently secure public Wi-Fi networks. The proposed CESA was based on a hash-based message authentication algorithm. A Digital Signature Algorithm (DSA) was accomplished to produce and verify signatures using the Secure Hash Algorithm (SHA). The Network Simulation-2 (NS-2) tool was used to evaluate the various settings of each algorithm, including key generation time, encryption time, and decryption time. Through the simulation, it was demonstrated that the proposed algorithm CESA outperformed both the Enhanced Diffie-Hellman (EDH) and Advanced Encryption Standard (AES) algorithms in terms of key generation time, encryption time, and decryption time. To generate the key, the proposed CESA algorithm took up to 59 s, while the EDH and AES algorithms took almost 90 s. To encrypt the data, the proposed CESA algorithm took about 98 seconds, while EDH and AES algorithms took almost 167 seconds. To decrypt the data, the proposed CESA algorithm took about 80 s, while EDH and AES algorithms took almost 160 s. Thus, the EDH and AES make CESA more robust against attacks and very rapid in handling encryption and decryption processes.