Description
Public-key cryptography has been widely employed for securing the digital world and
enabling critical applications. In constrained devices, dedicated co-processors provide
functionality required by popular schemes such as RSA and ECC. These schemes be-
came obsolete with the advent of the famous Shor’s algorithm that leverages the power
of quantum computers to break their fundamental assumptions. Quantum-resistent
schemes come as an answer to the threat of quantum computers to security by providing
new cryptographic constructs that do not rely on assumptions that the Shor’s algorithm
can invalidate. The large scale adoption of post-quantum cryptographic schemes that
were nominated to become the new standard is hindered by the fact that a large number
of them require different functionality than the old dedicated cryptographic processors
offer. Since these devices will still be in-use for many years to come, it is important to
secure them for the future by repurposing deployed cryptographic co-processors.
In this thesis we implement the Kronecker+ polynomial multiplication algorithm
tuned for the CRIYSTALS-Dilithium post-quantum, RLWE-based signature scheme, on
the OpenTitan Big Number Accelerator (OTBN). The Kroneker+ algorithm presented by
Bos et al. at USENIX 2022 builds on top of the functionality offered by common cryp-
tographic co-processors and enables efficient polynomial multiplication which is what
many new RLWE-based schemes such as Dilithium require. We benchmark the imple-
mentation for various parameter and compare the results with other implementations
of the chosen scheme.
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Thesis topic in co-operation with the Fraunhofer Institute for Applied and Integrated Security AISEC, Garching