Machine Learning Attacks and Countermeasures on Hardware Binary Edwards Curve Scalar Multipliers

Abstract

Machine Learning techniques have proven effective in Side Channel Analysis (SCA), enabling multiple improvements over the already-established profiling process of Template Attacks. Focusing on the need to mitigate their impact on embedded devices, a design model and strategy is proposed that can effectively be used as a backbone for introducing SCA countermeasures on Elliptic Curve Cryptography (ECC) scalar multipliers. The proposed design strategy is based on the decomposition of the round calculations of the Montgomery Power Ladder (MPL) algorithm and the Scalar Multiplication (SM) algorithm into the underlined finite field operations, and their restructuring into parallel-processed operation sets. Having as a basis the proposed design strategy, we showcase how advanced SCA countermeasures can be easily introduced, focusing on randomizing the projective coordinates of the MPL round’s ECC point results. To evaluate the design approach and its SCA countermeasures, several simple ML-based SCAs are performed, and an attack roadmap is provided. The proposed roadmap assumes attackers that do not have access to a huge number of leakage traces, and that have limited resources with which to mount Deep Learning attacks. The trained models’ performance reveals a high level of resistance against ML-based SCAs when including SCA countermeasures in the proposed design strategy.