Enhanced lattice-based signatures on reconfigurable hardware

Abstract

The recent Bimodal Lattice Signature Scheme (Bliss) showed that lattice-based constructions have evolved to practical alternatives to RSA or ECC. Besides reasonably small signatures with 5600 bits for a 128-bit level of security, Bliss enables extremely fast signing and signature verification in software. However, due to the complex sampling of Gaussian noise with high precision, it is not clear whether this scheme can be mapped efficiently to embedded devices. Even though the authors of Bliss also proposed a new sampling algorithm using Bernoulli variables this approach is more complex than previous methods using large precomputed tables. The clear disadvantage of using large tables for high performance is that they cannot be used on constrained computing environments, such as FPGAs, with limited memory. In this work we thus present techniques for an efficient Cumulative Distribution Table (CDT) based Gaussian sampler on reconfigurable hardware involving Peikert’s convolution lemma and the Kullback-Leibler divergence. Based on our enhanced sampler design, we provide a first Bliss architecture for Xilinx Spartan-6 FPGAs that integrates fast FFT/NTT-based polynomial multiplication, sparse multiplication, and a Keccak hash function. Additionally, we compare the CDT with the Bernoulli approach and show that for the particular Bliss-I parameter set the improved CDT approach is faster with lower area consumption. Our core uses 2,431 slices, 7.5 BRAMs, and 6 DSPs and performs a signing operation in 126 µs on average. Verification takes even less with 70 µs.