The Mysteries of LRA: Roots and Progress in Side-Channel Applications

Evaluating cryptographic implementations with respect to side-channel analysis (SCA) has been mandated at high security levels. Typically, the evaluation involves four stages: detection, modeling, certification and recovery. In pursuit of a specific goal at each stage, inherently different techniques were previously considered necessary. However, since the recent Eurocrypt 2022 and Eurocrypt 2024, linear regression analysis (LRA) has become the unique technique well-applied throughout all the stages. In this paper, we concentrate on this “silver bullet” technique within the field of SCA. In the first part of this paper, we answer three fundamental questions organized progressively. The first one relates to “why use LRA?”. Our discussion of the nominal and binary nature elucidates its critical role in underpinning the state-of-the-art techniques. Having understood the merits, a natural follow-up is “how to use it (correctly and effectively)?”. A theoretical analysis of the design matrix is provided, regarding the sample distribution of plaintext and the chosen degree of polynomial. We summarize the conditions for eliminating multicollinearity, a problem that can be harmful to all LRA-based techniques. The last question “who should use LRA?” reveals an intriguing evaluator-advantageous property: LRA can only unleash its full potential when the key is known. In the second part of this paper, we clarify the connections between LRA and traditional SCA techniques. Our proofs provide new insights into the prior investigation of SCA reduction, fostering a comprehensive understanding of this linear family. The conclusions suggest that the core working mechanisms of the state-of-the-art techniques can be traced back to those of earlier differential side-channel analyses. Experimental results are in line with the theory, confirming its correctness in practice.