Design And Hardware Implementation Of ECC Algorithm For Reconfigurable Computing

With the rapid development of the Internet,people pay more and more attention to the importance of information security.Cryptography can en sure the safety,confidentiality,integrity and no tampering of data in the process of communication.As one of the branches of cryptosystem,public key cryptosystem can effectively deal with digital signature,identity authentication,key distribution and other issues.Elliptic Curve Cryptography(ECC)has the advantages of high security,short key,fast processing speed and low loan requirement in the existing public key cryptosystem,and has a good application prospect.At present,ECC hardware implementation schemes are mostly designed for specific districts and counties to meet the increasing sec urity requirements.The low-complexity ECC scalar multiplication algorithm is studied,and the overall hardware design of the algorithm is completed by using re configurable computation architecture.Because the prime field has higher security than the binary field,this paper selects five prime field curves recommended by NIST,such as P521 and P384,as the curves used in the hardware design and implementation of reconfigurable computation.The main contents of this paper are as follows:1.On the basis of analyzing ECC's composition structure and common algorithm protocols,and concluding that the most time-consuming part is scalar multiplication for problems such as ECDSA and other protocols that need to use different single scalar multiplication and multiple scalar multiplication in the computation process,which lead to increased computational complexity,over-large multiplier area,over-large pretreatment amount of multi-base chain,etc.Based on the idea of Joint Multi-Base Chains(JMBC),a multi-scalar multiplication algorithm with low computational complexity is designed.The algorithm configurates the optimal multi-base chains,which can be used for different single scalar multiplication and multiple scalar multiplication algorithms.And the algorithm is modeled in Python,and the performance is evaluated on Core i5-9400 F @ 2.90 GHz six-core PC with Python V3.6.Experimental results showed that the the proposed algorithm is superior to existing algorithms in running speed and computational complexity,an d the number of preprocessing is reduced by 25% compared with w NAF and JSF.2.An ECC processing unit for reconfigurable computation is designed.The core idea of the processing unit design is the variation of Jordan-von Neumann's ideology.The overall structure of ECC is designed according to the Atithmetic and Logic Unit(ALU),Control Unit(CU)and Memory Unit(MU)respectively.In the design,the arithmetic operation units of ECC finite field layer such as point addition,double point and triple point,coordinate transformation,etc.,are used as ALU.And the control logic required for the operation of finite field layer is used as CU.A finite field operation ALU being suitable for multi-curve computation is designed,and this design is adopted by turns to improve the computation efficiency.Based on the designed multi-scalar multiplication algorithm with low computational complexity,the ECC top-level design is carried out,and the hardware architecture for reconfigurable ECC processing unit is obtained.Finally,the designed reconfigurable processing unit is modeled by Verilog,and simulated and DC logic synthesized by Modelsim.In CMOS process of TSMC 55 nm,the clock frequency of the circuit can reach to 250 MHZ,and the number of scalar multiplications can reach 100,000 times per second.In this paper,five prime field curves recommended by NIST are selected as the research objects.The designed multi-scalar multiplication algorithm with low computational complexity and reconfigurable computation architecture have certain theoretical guiding significance and great practical application value for ECC cryptography research.