Speeding up the execution-time of Crystals-Kyber PQC Algorithm on FPGA

Quantum computers have much more computing power than classical computers and this has created a challenge in the field of public-key cryptography algorithms, which is predicted quantum computers will reach the computational power to break existing public-key cryptography algorithms by 2030. To solve this problem, NIST published a call for post-quantum cryptography algorithms. Implementing these algorithms faces challenges such as execution time and resources. One of the algorithms that made it to the third round is the CRYSTALS-KYBER algorithm. In this algorithm, by optimizing the NTT module, the execution time is reduced. Usually, the implementation of NTT is created with radix-2, but in the proposed method, radix-4 is used, and this reduces the execution time. Changes to NTT are required to implement radix-4 NTT. DIT is used to implement NTT and DIF is used to implement INTT. In NTT and INTT formulas changes are made to the twiddle factors and the values of the twiddle factors stored to the ROM. In the following, we compared radix-4 butterfly unit with radix-2 butterfly unit. By reusing results in CT and GS butterfly units, we need four multiplications, additions, and subtractions, and the structure of radix-4 butterfly unit is mentioned. The memory unit uses eight RAMs to increase read and write speeds, four of which are for writing and the remaining four are for reading. It is also necessary to make corrections to the NTT parameters which are suitable for implementation on Kyber. Next, we implemented the proposed method on two FPGA Artix-7 and Virtex-7 using Vivado software. In the implementation on Artix-7 and Virtex-7 in exchange for a slight increase in the resources, the execution time in Artix-7 is reduced by 28.74% and 12.34% compared to similar implementations.