Computer Arithmetic for Cryptography and Reliable Security: Algorithms and Architectures

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Technology is accelerating, computing systems are becoming more powerful, and attackers are using sophisticated techniques and artificial intelligence. As a result, stronger security and cryptographic schemes with larger keys need to be implemented into smart devices and systems to protect sensitive data, computing systems, and network. The cryptographic systems are computationally complex and so their performance heavily relies on their efficient computations, specially in resource constrained embedded systems, such as smart cards, radio frequency identification tags, Internet of Things, and nodes in wireless sensor networks, where the power consumption, memory, and bandwidth are very limited. Efficient and reliable designs and implementations of cryptographic computations are challenging due to their complex nature. The main objective of this research is to propose novel computer arithmetic algorithms and architectures for cryptographic primitives and reliable security systems based on state of the art Advanced Encryption Standard (AES), the AES-GCM (Galois/counter mode) authenticated encryption, and Elliptic Curve Cryptography (ECC) as well as several submissions to the NIST lightweight cryptography standardization process. We are interested in devising the hardware implementations of such cryptographic systems for lightweight, low-power and high-speed target applications. We investigate the design of original algorithms and architectures for field arithmetic operations used in the AES, AES-GCM, and ECC cryptosystems. Choosing an appropriate field representation plays a critical role on the implementation performance of these cryptosystems. We consider different bases and representations to design the high-level and low-level arithmetic computations based on different design metrics. We investigate the effects of architectural design in terms of types of inputs and outputs (serial or parallel) and appropriate digit-level operations to find novel arithmetic algorithms/architectures with optimum digit sizes. Then, the optimum designs of the underlying arithmetic operations will be incorporated into the corresponding cryptosystems. Also, we design innovative reliable security systems to counteract natural faults and fault attacks. This research is very important for current and future technologies due to the increase in the density, clock frequency, and power dissipation per unit in very large scale integrated circuits. More importantly, fault attacks have become a serious concern in cryptography. This part of research will be based on adopting efficient concurrent error control coding approaches which has low overhead with acceptable error coverage. The outcome of this research leads to more secure and reliable cryptographic and security systems with lower cost and higher performance. It will also contribute to training highly qualified personnel for academia and Canadian industry.