@misc{Li2024, type = {Master Thesis}, author = {Li, Sze Hei}, title = {Distinguishability investigation on Longa's atomic patterns when used as a basis for implementing elliptic curve scalar multiplication algorithms}, doi = {10.26127/BTUOpen-6836}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-68366}, school = {BTU Cottbus - Senftenberg}, year = {2024}, abstract = {In the evolving landscape of cryptographic security, the robustness of Elliptic Curve Cryptography (ECC) against side-channel analysis (SCA) attacks is of paramount importance due to the widespread use of ECC and the growing sophistication of SCAs. This thesis delves into the investigation of Longa's atomic patterns applied within Elliptic Curve scalar multiplication algorithms, assessing their resistance to horizontal SCAs. The research employs these atomic patterns in practical implementation on a microcontroller (Texas Instruments Launchpad F28379 board) using the open-source cryptographic library FLECC in C. In our analysis, we only focused on the distinguishability of the first atomic block in the Elliptic Curve point doubling and point addition patterns. Due to various technical limitations, we were unable to determine significant differences in the execution time and the shapes of the atomic blocks. Further investigations of the SCA-resistance can be performed based on this work. A significant contribution of this work is the identification and correction of several discrepancies in Longa's original atomic patterns. This thesis marks the first practical implementation of Longa's patterns, extending the theoretical research into empirical analysis.}, subject = {Elliptic curve; Atomic patterns; Embedded devices; Scalar multiplication; Elliptische Kurve; Skalarmultiplikation elliptischer Kurven; Eingebettete Ger{\"a}te; Atommodelle; Atommodell; Elliptische Kurve; Multiplikation; Seitenkanalattacke; Mikrocontroller}, language = {en} } @misc{Doku2025, type = {Master Thesis}, author = {Doku, Philip Laryea}, title = {Investigation of the distinguishability of Giraud-Verneuil atomic blocks}, doi = {10.26127/BTUOpen-7140}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-71404}, school = {BTU Cottbus - Senftenberg}, year = {2025}, abstract = {In this work, we investigate the security of Elliptic Curve Cryptosystem (ECC) implementations against Side-Channel Analysis (SCA). ECC is well known for both its efficiency and strong security. However, it is also vulnerable to SCA. SCA exploits physical information leaked during the execution of the scalar multiplication (kP) operations. Countermeasures like regularity and atomicity have been developed against such attacks. This thesis, however, focuses on atomicity as a countermeasure. In this work, we focused on the atomic pattern proposed by Giraud and Verneuil used in the scalar multiplication operation. We implemented their atomic pattern using the right-to-left scalar multiplication algorithm on the P-256 elliptic curve, recommended by NIST. Our implementation was done using the FLECC cryptographic library, which supports constant-time operations, and it was executed on the Texas Instruments (TI) LAUNCHXLF28379D development board. We measured and collected the Electromagnetic (EM) emissions generated during the execution of the kP operation using measurement tools such as the Lecroy WavePro 604HD Oscilloscope, the Langer ICS 105 Integrated Circuit Scanner, and the Langer MFA-R 0.2-75 Near Field Probe. Our analysis focused on whether the Giraud and Verneuil atomic blocks could be distinguished based on their electromagnetic trace. We identified that when additionally inserted clock cycle processes were present in the execution, the atomic blocks could be visually distinguished from each other. However, after removing these processes, the atomic blocks became more synchronised and harder to distinguish, which reduced the risk of a successful SCA attack. These findings suggest that, although the atomic pattern was implemented correctly with dummy operations, its resistance to SCA can still be affected by the additional processes that are inserted on the hardware or software level. This means that atomicity alone as a countermeasure might not be enough to fully protect ECC implementations against SCA attacks. More research is required to investigate the reasons for the additionally inserted clock cycle processes that caused the distinguishability in the atomic blocks and also how intermediate operations are addressed in memory registers. This will help to better 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 offer useful results that can be used to improve countermeasures against SCA.}, subject = {Side Channel Analysis; Elliptic Curve Cryptosystem; Atomicity; Scalar Multiplication kP; FLECC; Kryptosystem; Elliptische Kurve; Seitenkanalattacke; Atomizit{\"a}t; Implementierung ; Elliptische-Kurven-Kryptosysteme; Seitenkanalanalyse; Skalarmultiplikation kP; Horizontale Seitenkanalangriffe; Atomare Bl{\"o}cke}, language = {en} }