On the Distinguishability of Chevallier-Mames Atomic Blocks in Binary kP Implementations

Atomic patterns were introduced as a lightweight countermeasure against simple side-channel analysis for elliptic curve scalar multiplication (kP) algorithms. By decomposing point operation into uniform atomic blocks, atomicity aims to ensure indistinguishability between point doubling and point addition, thereby preventing information leakage through observable executions. This thesis presents an experimental evaluation of Chevallier-Mames et al.’s on an embedded platform Texas Instruments LAUNCHXLF28379D development board using electromagnetic side-channel measurements. Three kP algorithms were implemented using the open-source FLECC cryptographic library: left-to-right double-and-add, right-to-left double-and-add and left-to-right with projective coordinate randomization. All three algorithms were implemented using the atomic patterns for elliptic curve point doubling and point addition operations corresponding to Chevallier-Mames. For each implemented algorithm, the distinguishability of the atomic blocks was evaluated by analyzing an electromagnetic (EM) trace of a single kP execution, i.e. performing a horizontal EM analysis. EM traces were captured for kP algorithm using a fixed 5-bit key and a template-based synchronization approach was developed to align atomic blocks within each single trace. The analysis shows that although atomicity improves resistance against simple visual inspection, distinguishable features remain observable in practice. In particular, consistent leakages were identified at the start of field multiplication operations, enabling classification of atomic blocks. Projective coordinate randomization mitigates data-bit leakage but did not eliminate structural leakage exploitable through horizontal analysis. The results demonstrate that atomic patterns alone do not guarantee indistinguishability in practical embedded implementations. This work highlights the importance of experimentally validating theoretical countermeasures under realistic EM side-channel conditions.