Chip Implementation And It's Security Defence For Elliptic Curve Cryptosystems Over GF(2~m)

The public key cryptography algorithm becomes the new direction of cryptography since it can solve the problem of identification, digital signature and the key distribution problems of the private key system for information security. Elliptic curve cryptography (Elliptic Curve Cryptosystem, ECC) is based on the problems of elliptic curve discrete logarithm, and is known as the next generation of public key cryptographic algorithms due to its selected key length can be smaller than that in RSA cryptosystems at the same level of security. However, due to the complexity of the ECC algorithm, in many applications a software implementation of ECC might be appropriate, but in some cases better performances are required and consequently hardware implementations should be used instead. Therefore, the first key problem is how to design the ECC chip for different platforms application. On the other hand, with the development of side channel analysis attacks, the implementation of ECC is faced with a serious security threaten. Therefore, the secure defence of ECC chip implementation became an important research topic. In this dissertation, the research focuses on the solutions of the two problems.Firstly, the elliptic curve over GF (2~m) is the research object since it is suitable for hardware implementation. In order to speed up scalar multiplication, the various various fast algorithms to reduce the operations of the finite field are compared. The result is that the Lopez-Dahab algorithm is the best algorithm compared to the various algorithms of the scalar multiplication. The top architecture and the operations of the finite field are important foundation of the implementation of the scalar multiplication algorithm.Secondly, the research on the finite field algorithms and implementation over GF (2~m) are carried out. Finite field multiplication is the bottleneck of scalar multiplication. In order to speed up computation speed, the finite field multiplication must be optimized for the high-performance solution of ECC. In order to solve the problem of the critical path delay of digit parallel multiplier increase with the number of digit, we propose to implement the multiplication by grouping in parallel base on the implementation of the serial, parallel and digit parallel multiplication. Thirdly, in order to solve the different requirements of the ECC application platform, the high-performance and the area and energy-constrained chip architecture are proposed. Three different high performance architectures are proposed, which are the optimized parallel architecture, the two multiplication parallel structures and the one multiplication structures. These three architectures have the advantage of resource or performance comparing to related literature. In the area and energy-constrained areas, such as wireless sensor network, the key problem is how to reducing the chip area and energy while the performance is requirements. In order to reduce the area, the top architecture is implemented by the serial. How to solve the problem of the optimal multiplication is the trade-off of between the area and the energy consumption. The optimized result is proposed comparing to the experiments.Finally, the side channel analysis attacks threaten the implementation of ECC badly. The security defence technology is very important. In this part, the research focus on the security defence technology of ECC through the experimentation platform. The ECC is implemented by serial structure. The Lopez-Dahab scalar multiplication algorithm can resist the simple power analysis attack through theory and experiments. However, it was proved that the Lopez-Dahab scalar multiplication algorithm and implementation can not resist the attack of differential power analysis by experiments. It is necessary to enhance the security defence measures for the implementation of the Lopez-Dahab algorithm. A new method of using redundant hardware technology is proposed to destroy the original Power curve base on the former researchers, which can achieve the purpose of security defence. It is proved by the experiments the measure can resist the difference power analysis attack.