Research On Key Technology Of Dual-Field Elliptic Curve Cryptography Coprocessor

Due to Elliptic Curve Cryptography(ECC)has the advantages of security strength,low power consumption and small storage space,it is widely used in the fields of identity authentication,fast encryption,digital signature,etc.However,the common ECC system can not solve the intercommunication problem because their finite field,elliptic curve and irreducible polynomial are different,therefore,the design of an ECC co-processor supporting dual field operation can solve this problem effectively.This paper mainly studies the key issues in the design of dual-field ECC co-processor.The core of elliptic curve cryptography is point multiplication,it is a top-down and step-by-step process.Based on this idea,we designed the ECC co-processor structure which can support the dual-field point operation module flexibly and the unit of dual-field modular operation are designed.Firstly,this paper made an in-depth study of ECC modular operation algorithm on the finite field,we embedded the addition without the carry chain operation of the binary field into the modular addition of prime field,based on this dual-field modular adder,a dual-field Montgomery modular multiplication scheme with variable step size is designed.Finally,designed the serial-parallel hybrid hardware implementation proposal corresponding to the algorithm structure,the scheme only needs0.31 us to perform a 256-bit prime field modular multiplication.And the throughput of the modular multiplier is at least 0.84 times higher than the existing literature.Then the paper focuses on the efficiency of point operations and algorithm parallelism in different coordinate systems of elliptic curve layer.A two-way parallel scheduling algorithm is proposed,which can increase the point double in the Jacobian coordinate system by 37%and the point addition in the Affine-Jacobi coordinate system by 10% on the prime field.At the same time,according to this scheduling method,the efficiency of point double in the LD coordinate system with the binary field has increased by 41%.The efficiency of point addition in the LD-Affine coordinates has increased by 26%.Finally,the proposed dual-field ECC co-processor of this design can perform prime field and binary field point multiplication operations,point addition and point double operations,modular multiplication and modular inverse operations according to the instruction set sent by the host system.In addition,the computational module of this design does not use any dedicated multiplier inside the device,so it has good portability which can make this dual-field ECC co-processor more flexible.This paper mainly aimed at the key technologies of ECC co-processors supporting dual-field operations.Combined with the characteristics of elliptic curve cryptography data processing,we designed a high performance ECC co-processor that supports prim and binary field operations from both the view of point arithmetic unit on the elliptic curve group and the modular operation unit on the finite field.It can cooperate with the host system to perform many kinds of ECC operations.