Study Of Coprocessor For SM2 Fast Scalar Multiplication

As the development and the prevalence of the computer network and the communication technology, wireless sensor network nodes, RFID tags, medical implants, and smart cards will have a central role in actualizing concepts such as the Internet of Things and, hence, providing strong cryptography with low resources has been an extremely active research field in the recent years.Elliptic curve cryptography (ECC) is one of the prime candidates for bringing public-key cryptography to applications with strict constraints on implementation resources such as power, energy, circuit area, memory, etc.The State Encryption Administration published a new commercial en-cryption algorithm, SM2 public key cryptography algorithm, to replace the RSA algorithm which is widely used in China. SM2 takes many advantages of RSA such as a shorter key, a faster processing speed and so on. Hence, SM2 algorithm is an excellent algorithm with high safety and practicality.The paper provides the frequently-used methods for F2m. We optimize the multiplier and the inverter to get a better result. According the analysis about the algorithms for ECC, we choose the Comb algorithm to compute the scalar multiplication. Karatsuba algorithm and the combination of Se-rial multiplier and Parallel multiplier are used for the multiplication in F2m. We construct circuits to compute the modular square in a clock period. For avoiding the modular inverse circuits cost, we compute the modular inverse by Fermat’s Theorem. Since having the modular square circuits and avoiding the modular inverse, we compute the scalar multiplication in Jacobian projective coordinates system. Since the number of scalar multiply for fixed point is more than others in SM2, we choose the Comb algorithm with 32 times point-add and point-double. We describe the architecture by using Verlog and simulate it with ModolSim SE 10.0a. Computing one point multiplication requires in total 7528 clock cycles.The paper is structured as follows. In Chapter 1, we give an simple introduction to SM2 and Coprocessor. Then in Chapter 2, we provide a brief background on F2m. Parameters and Safety Analysis for SM2 are presented in Chapter 3. We describe point multiplication algorithm and our improvement in Chapter 4. We provide synthesis results and end with conclusions in Chapter 5.