Research and Design of Hardware Circuit for Elliptic Curve Cryptographic Algorithm

Accompanied by the development of computer technology, cryptography has become a key technology to ensure information security. Elliptic curve cryptographic algorithm has been the key research object of cryptographers in recent years, and SM2 algorithm, as a cryptographic algorithm independently developed by China, has great advantages in algorithmic performance and other aspects. Based on SM2 algorithm, this paper realizes the hardware design of four functions: decryption, encryption, digital signature verification and digital signature. The scalar multiplication module is the core module in SM2 algorithm, and the performance of scalar multiplication module determines the performance of SM2 algorithm. In this paper, we first analyze and design the NAF -based scalar multiplication module, which reduces the number of point addition operations and thus shortens the operation time of the scalar multiplication module, and then process the point doubling and point addition modules called by scalar multiplication, and then design the parallel point doubling and point addition operation circuits based on the Jacobian projective coordinate system, which shortens the operation time of the point doubling and point addition modules, after deeply investigating the data flow in the Jacobian projective coordinate system. Finally, we also design parallel modulo multiplication circuits to shorten the computation time of the modulo multiplication module. The main contribution of this paper in improving the performance of the scalar multiplication module is the simultaneous optimization of the elliptic curve arithmetic layer and the modulo multiplication arithmetic layer, which greatly reduces the computation time of the scalar multiplication module, and is verified on the Xilinx Virtex-7, and the experimental results show that the speed of the optimized scalar multiplication module has been significantly improved.