KiD: A Hardware Design Framework Targeting Unified NTT Multiplication for CRYSTALS-Kyber and CRYSTALS-Dilithium on FPGA

Large-degree polynomial multiplication is an integral component of post-quantum secure lattice-based cryptographic algorithms like CRYSTALS-Kyber and Dilithium. The computational complexity of large-degree polynomial multiplication can be reduced significantly through Number Theoretic Transformation (NTT). In this paper, we aim to develop a unified and shared NTT architecture that can support polynomial multiplication for both CRYSTALS-Kyber and Dilithium. More specifically, in this paper, we have proposed three different unified architectures for NTT multiplication in CRYSTALS-Kyber and Dilithium with varying numbers of configurable radix-2 butterfly units. Additionally, the developed implementation is coupled with a conflict-free memory mapping scheme that allows the architecture to be fully pipelined. We have validated our implementation on Artix-7, Zynq-7000 and Zynq Ultrascale+ FPGAs. Our standalone implementations for NTT multiplication for CRYSTALS-Kyber and Dilithium perform better than the existing works, and our unified architecture shows excellent area and timing performance compared to both standalone and existing unified implementations. This architecture can potentially be used for compact and efficient implementation for CRYSTALS-Kyber and Dilithium.