A Comparative Analysis of the Computation Cost and Energy Consumption of Relevant Curves of ECC Presented in Literature

Abstract

With the Internet of Things (IoT) becoming expo-nentially more prevalent, the need for lightweight cryptography functions increases simultaneously. Namely, IoT end devices are mostly limited by their resource-constrained capabilities and therefore cannot rely on heavyweight cryptographic algorithms such as Rivest-Shamir-Adleman (RSA) or Diffie-Hellman (DH) for security. Elliptic Curve Cryptography (ECC) offers a more lightweight alternative by being based on a mathematical prob-lem named the Elliptic Curve Discrete Logarithm Problem (ECDLP) which is not known to be solvable in sub-exponential time. Within the field of ECC, many different curve types exist following various standards for this protocol. In this paper, the energy consumption and time consumption for key generation, encryption, and decryption are measured within the ElGamal protocol using ECC for the various curves. To measure this, a Raspberry Pi 4B and a Personal Computer are used to conclude the disproval of the hypothesis that the Twisted Edwards curve performs most efficient to achieve its security strength. Namely, Brainpool curves function most efficient within this benchmark, after which Short Weierstrass curves follow. Moreover, it is concluded the performance pattern for both data processors and data providers is equal to each other for all message sizes.