SM2-based low-cost and efficient parallel modular multiplication

Elliptic curve encryption (ECC) has been widely used in public key cryptography, and modular multiplication is one of the core operations of elliptic curve encryption. This paper presents a low-cost high-speed parallel modular multiplication implementation based on SM2. Using the characteristics of the prime (P256), the two-step multiplication and reduction of modular multiplication are performed in parallel. The 8-part karatsuba algorithm is used in multiplication. In the process of performing multiplication, in order to reduce the consumption of multiplier resources, the karatsuba algorithm is used to improve the ordinary multiplier. The control signal EN=0/1 is used to control the multiplier to perform ordinary multiplication or karatsuba algorithm multiplication. Then the multiplier is reused. 4 improved 32-bit multipliers are used in complete 256-bit modular multiplication. Experiments show that on the 100 MHz Artix-7 FPGA hardware platform, only 12K LUTs are needed, and a modular multiplication operation can be completed in 0.09μs. Comprehensive time and area, our design has certain advantages.