Energy Efficiency Analysis of Elliptic Curve Based Cryptosystems

Energy consumption is an important factor for any cryptoscheme, implemented on devices having limited energy resource. In this paper, we analyze the energy consumption during the Diffie-Hellman key exchange implemented on both supersingular and ordinary elliptic curves. The former protocol is Supersingular Isogeny based Diffie-Hellman (SIDH) and the latter is Elliptic Curve based Diffie-Hellman (ECDH) respectively. Implementations are executed on 64 bit Intel Skylake processor. The energy consumption is analysed for the classical bit security levels of 128 and 192. In this paper, a detailed comparison of power and energy consumption by elliptic curve point addition and doubling operations is presented for affine and standard projective coordinates. Projective coordinates based elliptic curve operations are found to be around 50 to 60 times more energy efficient. We then analyze SIDH and ECDH, implemented using projective coordinates. Our results show that, SIDH consumes around 37 to 47 times more energy in comparison to ECDH for the above mentioned bit security levels.