  This paper presents a comparative analysis between the Genetic Algorithm (GA)
and Particle Swarm Optimization (PSO), two vital artificial intelligence
algorithms, focusing on optimizing Elliptic Curve Cryptography (ECC)
parameters. These encompass the elliptic curve coefficients, prime number,
generator point, group order, and cofactor. The study provides insights into
which of the bio-inspired algorithms yields better optimization results for ECC
configurations, examining performances under the same fitness function. This
function incorporates methods to ensure robust ECC parameters, including
assessing for singular or anomalous curves and applying Pollard's rho attack
and Hasse's theorem for optimization precision. The optimized parameters
generated by GA and PSO are tested in a simulated e-commerce environment,
contrasting with well-known curves like secp256k1 during the transmission of
order messages using Elliptic Curve-Diffie Hellman (ECDH) and Hash-based
Message Authentication Code (HMAC). Focusing on traditional computing in the
pre-quantum era, this research highlights the efficacy of GA and PSO in ECC
optimization, with implications for enhancing cybersecurity in third-party
e-commerce integrations. We recommend the immediate consideration of these
findings before quantum computing's widespread adoption.
