Sustainable cryptography: Carbon asymmetry in partially homomorphic encryption in the cloud

Abstract

Encryption protects data in the cloud but adds energy cost, especially for partially homomorphic encryption (PHE) schemes that allow computation on encrypted data. Their carbon footprint across cloud data center deployments remains underexplored. We benchmark eight PHE algorithms from the LightPHE open-source Python library, including RSA, ElGamal, Exponential ElGamal, Paillier, Damg & aring;rd-Jurik, Okamoto-Uchiyama, Goldwasser-Micali, and Elliptic Curve ElGamal, across six cloud environments, and use timing data as input to a carbon estimation model covering Scope 1, Scope 2, and Scope 3 emissions across ten data center configurations. We ground the energy model with a dedicated Intel RAPL calibration on bare-metal hardware using 30 repetitions per configuration. The calibration measures average CPU package power at 34.7 W and total system power at 48.4 W, showing that a fixed 150 W CPU-only assumption overestimates actual CPU power by a factor of 4.3. We present calibrated estimates alongside a 150 W server-class scenario and a sensitivity analysis across power, PUE, and grid carbon intensity. Elliptic curve schemes provide equivalent classical security at a fraction of the energy cost of RSA, and algorithm-specific mathematical structure drives order-of-magnitude differences in carbon output. These results reveal an asymmetry between security and carbon cost across PHE algorithms and establish a sustainable-cryptography baseline for future PQC-based homomorphic schemes.