Time-Memory Trade-Offs for Saber+ on Memory-Constrained RISC-V Platform

Abstract

Saber is a module-lattice-based key encapsulation scheme that has been selected as a finalist in the NIST Post-Quantum Cryptography standardization project. As Saber computes on considerably large matrices and vectors of polynomials, its efficient implementation on memory-constrained IoT devices is very challenging. In this paper, we present an implementation of Saber with a minor tweak to the original Saber protocol for achieving reduced memory consumption and better performance. We call this tweaked implementation ‘Saber+’, and the difference compared to Saber is that we use different generation methods of public matrix <inline-formula><tex-math notation="LaTeX">$\boldsymbol{A}$</tex-math></inline-formula> and secret vector <inline-formula><tex-math notation="LaTeX">$\boldsymbol{s}$</tex-math></inline-formula> for memory optimization. Our highly optimized software implementation of Saber+ on a memory-constrained RISC-V platform achieves 48% performance improvement compared with the best state-of-the-art memory-optimized implementation of original Saber. Specifically, we present various memory and performance optimizations for Saber+ on a memory-constrained RISC-V microcontroller, with merely 16KB of memory available. We utilize the Number Theoretic Transform (NTT) to speed up the polynomial multiplication in Saber+. For optimizing cycle counts and memory consumption during NTT, we carefully compare the efficiency of the complete and incomplete-NTTs, with platform-specific optimization. We implement 4-layers merging in the complete-NTT and 3-layers merging in the 6-layer incomplete-NTT. An improved on-the-fly generation strategy of the public matrix and secret vector in Saber+ results in low memory footprint. Furthermore, by combining different optimization strategies, various time-memory trade-offs are explored. Our software implementation for Saber+ on selected RISC-V core takes just 3,809K, 3,594K, and 3,193K clock cycles for key generation, encapsulation, and decapsulation, respectively, while consuming only 4.8KB of stack at most.