The Improved Montgomery Scalar Multiplication Algorithm with DPA Resistance

With Montgomery scalar multiplication algorithm being widely used in elliptic curve cryptography systems, the researches on DPA attacks against Montgomery scalar multiplication algorithm become more extensive, but few researches are about the DPA resistance algorithm. This paper analyzed the DPA resistance capability of the Montgomery scalar multiplication algorithm firstly, and on this basis, proposed an improved algorithm with random Z coordinate to resist the DPA attacks with the characteristics that the parameter Z only participates in the intermediate operations without affecting the final results. This paper described the original algorithm and the improved algorithm using Verilog HDL targeting on the 65 nm standard cell library. Results show that the improved Montgomery Scalar Multiplication algorithm can dramatically improve the anti-DPA attack property with only 0.36% performance and area 9.60% area penalty.