With the increasing need to protect information digitally, the study of cryptography has become of paramount importance. The digital world requires strong and efficient encryption algorithms in order to ensure private information are not compromised. As we strive towards making our devices smaller, the cost of the cryptographic implementation becomes more significant. In this thesis, we will look at new optimising algorithms to reduce the number of exclusive or (XOR) boolean operations in the workhorses algorithms for encryption. The algorithms presented in this thesis are new and based on an improved version of the Boyar and Peralta's algorithm. It was motivated by a graph search approach to find a path towards the various targets. We will be drawing comparisons to the results obtained by various algorithms out there such as Paar's algorithm, Boyar and Peralta's algorithm. Overall, the results obtained from the new heuristic showed that this algorithm fares better than those mentioned above. Master of Science