📝 SummarXiv

Abstract

In this work, we investigate the security of Elliptic Curve Cryptosystem (ECC) implementations against Side-Channel Analysis (SCA). ECC is well known for its efficiency and strong security, yet vulnerable to SCA which exploits physical information leaked during scalar multiplication (kP). Countermeasures such as regularity and atomicity exist; this thesis focuses on atomicity. In this work, we study the Giraud and Verneuil atomic pattern for kP, implementing it using the right-to-left kP algorithm on the NIST EC P-256 curve. We use the FLECC library with constant-time operations and execute on the Texas Instruments LAUNCHXLF28379D MCU. We measure Electromagnetic (EM) emissions during kP using a Lecroy WavePro 604HD Oscilloscope, a Langer ICS 105 Integrated Circuit Scanner, and a Langer MFA-R 0.2-75 Near Field Probe. We investigate whether the Giraud and Verneuil atomic blocks are distinguishable in EM traces. Our findings show that, when additional clock cycle processes are present, the atomic blocks can be visually distinguished; after removing these processes, they become more synchronised and harder to distinguish, reducing the risk of a successful SCA attack. These results show that, although the atomic pattern is correctly implemented with dummy operations, resistance to SCA can still be affected by additional processes inserted at hardware or software level.This means atomicity alone may not fully protect ECC from SCA. More research is needed to investigate the causes of the additional clock cycle processes and how intermediate operations are addressed in memory registers. This will help to understand the processes that lead to the insertion of these additional clock cycles. This thesis is the first to experimentally implement and investigate Giraud and Verneuil's atomic pattern on hardware, and it offers useful results to improve countermeasures against SCA.