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.

翻译：本研究旨在探究椭圆曲线密码系统（ECC）实现方案在面对侧信道分析（SCA）时的安全性。ECC以其高效性和强安全性著称，但在执行标量乘法（kP）过程中泄露的物理信息使其易受SCA攻击。现有防护措施包括规则化与原子化，本文聚焦于原子化方案。本研究针对kP运算中的Giraud与Verneuil原子化模式，在NIST EC P-256曲线上采用从右至左的kP算法进行实现。我们使用具备恒定时间运算特性的FLECC密码库，在德州仪器LAUNCHXLF28379D微控制器上执行算法。通过力科WavePro 604HD示波器、Langer ICS 105集成电路扫描仪及Langer MFA-R 0.2-75近场探头，采集kP运算过程中的电磁辐射信号。我们重点探究Giraud与Verneuil原子块在电磁轨迹中是否具有可区分性。实验结果表明：当存在额外时钟周期处理时，原子块在视觉上可被区分；消除这些额外处理后，原子块同步性增强且更难区分，从而降低了SCA攻击的成功风险。这些发现表明，即使正确实现了包含虚拟操作的原子化模式，硬件或软件层面插入的额外处理仍可能影响其对SCA的抵御能力。这意味着仅靠原子化方案可能无法完全保护ECC免受SCA攻击。未来需进一步探究额外时钟周期处理的成因及内存寄存器中中间操作的寻址机制，以深入理解导致额外时钟周期插入的处理过程。本论文首次通过实验在硬件平台上实现并研究了Giraud与Verneuil原子化模式，为完善SCA防护措施提供了有价值的参考依据。