Abstract:
Multivariate cryptosystems belong to the five most promising families of post-quantum
cryptography (PQC) schemes. Among them, the Unbalanced Oil and Vinegar (UOV) and
the Rainbow signature schemes have been extensively studied since 1999 and 2005, respectively.
The main advantage of UOV is high confidence in its security; the disadvantages
include large key and signature sizes. Rainbow is a multi-layer version of UOV that offers
better performance, smaller keys, and smaller signatures. In this thesis, we present and compare
hardware implementations of both schemes in high-performance Field Programmable
Gate Arrays (FPGAs). The optimization is for the minimum signature generation and
verification time. The generation of keys is assumed to be done in software. Compared to
the previous state-of-the-art high-speed implementation, the proposed design for Rainbow
is more than twice as fast, and introduces two architectural innovations: a novel pivot calculation
circuit and a memory based microprogrammed architecture. Additionally, in order
to make benchmarking easier and fairer, our design follows a universal PQC hardware API,
which allows for fair comparison with other post-quantum signature schemes, in particular
those submitted to the NIST PQC Project. The design is intended to be made open-source
to speed-up further optimizations. Additionally, we will provide a projection of scalability
for larger security levels and future optimizations.
