This guided research will study the rigorous speed-up that quantum kernels provide to tackle classically intractable problems - in this case, the discrete logarithm problem - and then provide a potential implementation, test it on inputs of various complexity and show the current challenges to finding the proper concrete form of the circuit for the quantum kernel and implement it. The experiments are conducted in Python using Qiskit and cvxopt for the classical convex optimization problem that Support Vector Machines solve.