Design And Implementation Research Of Accelerator For ECC Over GF(2~m)

Public key cryptographic technology plays a very important role in the field of information security. The security of Elliptic Curve Cryptography(ECC) is based on the difficulty of elliptic curve discrete logarithm, and it provides the highest security strength per bit than any other currently existing public key cryptosystem. Besides, ECC supplies more flexibility and expansibility in application, thus it has attracted more and more researchers.Firstly, basing on the research of ECC algorithms selves' characteristics, and facing to desktop applications which aim at System on Chip(SoC), a fast design scheme of a universal accelerator for GF(2~m) is given in this paper. Then under the analysis of point multiplication algorithms and coordinates, a software and hardware co-design scheme of point multiplication is proposed. At last the ECC system implemented by above schemes is integrated into SoC.This paper has following contributions:1. After extensive research on all kinds of affine coordinate and project coordinates, a new mixed coordinate is fabricated. Time complexity of point multiplication under mixed coordinate shows that it has 2.3%～12.3% higher efficiency than any other project coordinate at least.2. In this paper, archtecture and interface of a SoC oriented accelerator for GF(2~m) are given, and its extensible scope is 160≤m≤400. Using the configurable control instructions, the accelerator is well suitable for the implementation of operations on elliptic curves, such as point addition, point double and so on.3. The inverse operation in GF(2~m) holds the balance in ECC. Under the comparison of two inverse algorithms, a selected algorithm is improved. The implemetation result indicates that the improved algorithm has perfect performance.4. The universal accelerator for GF(2~m) is implemented based on FPGA devices of Altera, and the implementation of point multiplication is completed by the microcode instructions. The results of FPGA test manifest that it not only provides higher computing performance than any other product at home, but also has many other merits, such as lower power, higher security, larger extensibility and so on. What's more, the fast implementation of an accelerator for big integer operations is achieved. At the present time, it is used in public key cryptographic equipment by some graduate institute.