A Software/Hardware Co-Design of Crystals-Dilithium Signature Scheme

Abstract

As quantum computers become more affordable and commonplace, existing security systems that are based on classical cryptographic primitives, such as RSA and Elliptic Curve Cryptography (ECC), will no longer be secure. Hence, there has been interest in designing post-quantum cryptographic (PQC) schemes, such as those based on lattice-based cryptography (LBC). The potential of LBC schemes is evidenced by the number of such schemes passing the selection of NIST PQC Standardization Process Round-3. One such scheme is the Crystals-Dilithium signature scheme, which is based on the hard module-lattice problem. However, there is no efficient implementation of the Crystals-Dilithium signature scheme. Hence, in this article, we present a compact hardware architecture containing elaborate modular multiplication units using the Karatsuba algorithm along with smart generators of address sequence and twiddle factors for NTT, which can complete polynomial addition/multiplication with the parameter setting of Dilithium in a short clock period. Also, we propose a fast software/hardware co-design implementation on Field Programmable Gate Array (FPGA) for the Dilithium scheme with a tradeoff between speed and resource utilization. Our co-design implementation outperforms a pure C implementation on a Nios-II processor of the platform Altera DE2-115, in the sense that our implementation is 11.2 and 7.4 times faster for signature and verification, respectively. In addition, we also achieve approximately 51% and 31% speed improvement for signature and verification, in comparison to the pure C implementation on processor ARM Cortex-A9 of ZYNQ-7020 platform.