In light of the recent emergence of quantum computing and the consequent threat to classical cryptographic platforms, this paper presents a new Boolean Key Exchange Protocol and the incorporation of the BLAKE3 cryptographic hash function. It employs a security mechanism based on the non-linearity and non-invertibility of Boolean algebra alongside an improved flexibility and efficiency of the BLAKE3 hash function to provide the defense against quantum threats. The new protocol offered better operational performance than the Tropical Key-Exchange protocol. Compared with other post-quantum cryptographic protocols, such as Kyber FrodoKem, HQC, BIKE, NTRU-Prime, and NewHope, the new protocol offered a better balance between performance and memory efficiency. The results are validated, showing how it is possible to successfully apply the protocol and attain security while incurring low computation and memory costs, making it one of the best probable solutions for secure communication in the future quantum computing environment.