Yes / Scouring around the bridge pier is a natural and complex phenomenon that results in bridge failure. Failure of bridges have potential devastation and public safety and economic loss, which lead to political consequences and environmental impacts. Therefore, it is essential to countermeasure the scour around the bridge pier. This paper studies the effects of four different airfoil-shaped collars (i.e., bc1 = 1.5b, bc2 = 2.0b, bc3 = 2.5b and bc4 = 3.0b, where bc and b are the diameter of the airfoil-shaped collar and pier, respectively) as a scour countermeasure. All the experiments are conducted under clear water conditions with uniform sediment and a constant water depth (y) of 10 cm. Airfoil-shaped collar is placed at four elevations, i.e., bed level, y/4, y/2 and 3y/4 above the sediment bed level. It is observed that the maximum percentages of scour reduction of 86, 100 and 100% occurred due to protection provided by the collar bc2, bc3 and bc4, respectively, at sediment bed level. So, collars bc2, bc3 and bc4 are efficient at the sediment bed level. The profiles of scour hole show that the length of the transverse scour hole is greater than that of the longitudinal one. Numerical investigation of the morphological changes in sediment bed and scour depth contours is developed using the FLOW-3D for the pier with and without the airfoil-shaped collar.

This PhD thesis focuses on the study, the hardware design, the theoretical and practical validation, and eventually the comparison of different arithmetic operators for cryptosystems based on elliptic curves (ECC). Provided solutions must be robust against some side-channel attacks, and efficient at a hardware level (execution speed and area). In the case of ECC, we want to protect the secret key, a large integer, used in the scalar multiplication. Our protection methods use representations of numbers, and behaviour of algorithms to make more difficult some attacks. For instance, we randomly change some representations of manipulated numbers while ensuring that computed values are correct. Redundant representations like signed-digit representation, the double- (DBNS) and multi-base number system (MBNS) have been studied. A proposed method provides an on-the-fly MBNS recoding which operates in parallel to curve-level operations and at very high speed. All recoding techniques have been theoretically validated, simulated extensively in software, and finally implemented in hardware (FPGA and ASIC). A side-channel attack called template attack is also carried out to evaluate the robustness of a cryptosystem using a redundant number representation. Eventually, a study is conducted at the hardware level to provide an ECC cryptosystem with a regular behaviour of computed operations during the scalar multiplication so as to protect against some side-channel attacks.

Cette thèse porte sur l'étude, la conception matérielle, la validation théorique et pratique, et enfin la comparaison de différents opérateurs arithmétiques pour des cryptosystèmes basés sur les courbes elliptiques (ECC). Les solutions proposées doivent être robustes contre certaines attaques par canaux cachés tout en étant performantes en matériel, tant au niveau de la vitesse d'exécution que de la surface utilisée. Dans ECC, nous cherchons à protéger la clé secrète, un grand entier, utilisé lors de la multiplication scalaire. Pour nous protéger contre des attaques par observation, nous avons utilisé certaines représentations des nombres et des algorithmes de calcul pour rendre difficiles certaines attaques ; comme par exemple rendre aléatoires certaines représentations des nombres manipulés, en recodant certaines valeurs internes, tout en garantissant que les valeurs calculées soient correctes. Ainsi, l'utilisation de la représentation en chiffres signés, du système de base double (DBNS) et multiple (MBNS) ont été étudiés. Toutes les techniques de recodage ont été validées théoriquement, simulées intensivement en logiciel, et enfin implantées en matériel (FPGA et ASIC). Une attaque par canaux cachés de type template a de plus été réalisée pour évaluer la robustesse d'un cryptosystème utilisant certaines de nos solutions. Enfin, une étude au niveau matériel a été menée dans le but de fournir à un cryptosystème ECC un comportement régulier des opérations effectuées lors de la multiplication scalaire afin de se protéger contre certaines attaques par observation. / This PhD thesis focuses on the study, the hardware design, the theoretical and practical validation, and eventually the comparison of different arithmetic operators for cryptosystems based on elliptic curves (ECC). Provided solutions must be robust against some side-channel attacks, and efficient at a hardware level (execution speed and area). In the case of ECC, we want to protect the secret key, a large integer, used in the scalar multiplication. Our protection methods use representations of numbers, and behaviour of algorithms to make more difficult some attacks. For instance, we randomly change some representations of manipulated numbers while ensuring that computed values are correct. Redundant representations like signed-digit representation, the double- (DBNS) and multi-base number system (MBNS) have been studied. A proposed method provides an on-the-fly MBNS recoding which operates in parallel to curve-level operations and at very high speed. All recoding techniques have been theoretically validated, simulated extensively in software, and finally implemented in hardware (FPGA and ASIC). A side-channel attack called template attack is also carried out to evaluate the robustness of a cryptosystem using a redundant number representation. Eventually, a study is conducted at the hardware level to provide an ECC cryptosystem with a regular behaviour of computed operations during the scalar multiplication so as to protect against some side-channel attacks.